Chapter 3

loss data must be consistent in at least two respects

1.the loss data must be collected on a consistent basis for all recorded losses 2.data must be expressed in constant dollars, to adjust for differences in price levels.

Understanding the cumulative probability distribution will enable an analyst to evaluate the effect of various Select one: A. Deductibles and policy limits on insured loss exposures. B. Modification factors in terms of accuracy for trending purposes. C. Types of losses and their impact on policyholder surplus. D. Types of available insurance and coverages for specific loss exposures.

A. Deductibles and policy limits on insured loss exposures.

The relationship between the expected value and the standard deviation of a normal distribution can have useful practical application. Which one of the following best describes such a practical application? Select one: A. Determining a maintenance schedule for equipment that could become dangerous if it were to fail B. Identifying whether a particular loss exposure is high-frequency and low-severity, or high-severity and low frequency C. Selecting which risk management technique would be most appropriate for a particular loss exposure D. Predicting when losses, such as physical damages losses to an automobile fleet, are likely to occur

A. Determining a maintenance schedule for equipment that could become dangerous if it were to fail Correct. Determining a maintenance schedule for equipment that could become dangerous if it were to fail best describes such a practical application.

The extent to which a distribution is spread out rather than concentrated around the expected value is its Select one: A. Dispersion. B. Concentration. C. Tendency. D. Density.

A. Dispersion.

Which one of the following describes the law of large numbers? Select one: A. It states that as the number of similar but independent exposure units increases, the relative accuracy of predictions about future outcomes also increases. B. It states that the more times a particular event has occurred in the past, the greater the likelihood of that same event occurring in the future. C. It states that events that have occurred in the past under identical conditions and resulting from unchanging causal forces will increase at a predictable rate into the future. D. It states that, in order to be able to predict the relative probability of future events, those events must be both frequent, and independent of one another.

A. It states that as the number of similar but independent exposure units increases, the relative accuracy of predictions about future outcomes also increases.

In loss analysis, the Prouty Approach primarily involves Select one: A. Loss frequency and severity. B. Loss timing. C. Total dollar loss values. D. Loss credibility.

A. Loss frequency and severity.

To determine which one of the following measures must the values in a data set be arranged by size? Select one: A. Median B. Mean C. Expected value D. Mode

A. Median

Insurance and risk management professionals use which one of the following methods to evaluate the variability around the mean and apply it to business decisions? Select one: A. Normal probability distributions B. Asymmetrical distributions C. Theoretical continuous distributions D. Measures of dispersion

A. Normal probability distributions

Hank has determined the expected number of workers compensations claims in a given year. Hank next calculates the standard deviation of potential outcomes. Calculating the standard deviation Select one: A. Provides a measure of how sure Hank can be in his estimate of claims. B. Allows Hank to accurately predict the mean of the distribution. C. Allows Hank to estimate accurate claim reserves for future workers compensation claims. D. Enables the organization to make better use of its resources.

A. Provides a measure of how sure Hank can be in his estimate of claims.

When developing loss severity distributions, risk professionals should organize loss data by Select one: A. Size of loss. B. Location of loss. C. Time of loss. D. Date of loss.

A. Size of loss.

Which one of the following describes the two ways in which loss data must be consistent to accurately estimate future loss exposures? Select one: A. The data must be collected on a consistent basis for all recorded losses, and the data must be expressed in constant dollars. B. The past losses under analysis must all have occurred during the same time period and at the same location. C. The loss values used must be actual amounts paid rather than estimates or reserves and should be expressed in current dollars. D. The data must come from an organization's own records rather than other sources, and it should be categorized by severity of loss.

A. The data must be collected on a consistent basis for all recorded losses, and the data must be expressed in constant dollars.

The table below represents the probability distribution of auto physical damage losses for a fleet of insured vehicles. Which one of the following statements is correct with respect to the information it provides? size of loss # of losses % of # of losses $0-$5k 8 40% $5,001-$10k 7 35% $10,001-$15k 2 10% $15,001-$20k 2 10% $20,001 + 1 5% total 20 100% Select one: A. There is a 40 percent probability of any loss being $5,000 or less. B. Maintaining a $5,000 deductible would eliminate 40 percent of total dollar losses. C. This represents a theoretical probability distribution. D. This represents a discrete probability distribution.

A. There is a 40 percent probability of any loss being $5,000 or less.

Which one of the following statements is correct with respect to the completeness of past loss data when estimating future loss exposures? Select one: A. What constitutes complete loss data depends largely on the nature of the loss exposure being considered. B. While having complete loss data is helpful, it is not one of the four criteria considered necessary to accurately analyze loss exposures. C. Having complete information on losses helps isolate the causes of loss, but is of little use for estimating the value of future losses. D. Loss data is considered to be complete if it relates to past claims that are substantially the same as the potential future claims being assessed.

A. What constitutes complete loss data depends largely on the nature of the loss exposure being considered.

Which one of the following statements is true regarding characteristics of normal distributions? Select one: A. When graphed, a normal distribution generates a bell-shaped curve. B. The normal curve touches the horizontal line at the base of the distribution at only two points. C. In theory, the normal distribution assigns some negative probability no greater than zero for every outcome. D. Insurers cannot use normal probability distributions to predict future losses but they are able to use them to control or mitigate future losses.

A. When graphed, a normal distribution generates a bell-shaped curve.

A risk professional may use dispersion to compare the characteristics of probability distributions. Which one of the following statements is true in this regard? Select one: A. When two or more distributions are plotted on a graph, the one with the most sharply peaked curve has the smallest standard deviation. B. The greater the dispersion around a distribution's expected value, the greater the likelihood that actual results will fall within a given range of that expected value. C. When a distribution is plotted on a graph, the more dispersed the distribution is, the more sharply peaked the curve is. D. In general, the less dispersion around the central tendency, the more risk is involved in the exposure.

A. When two or more distributions are plotted on a graph, the one with the most sharply peaked curve has the smallest standard deviation.

categories of loss frequency ion the Prouty Approach

Almost Nil Slight Moderate Definite

In an array of 10 losses, if expected loss frequency is 4.2 when expected loss severity is $200.50, the expected total dollar loss is Select one: A. $86.10. B. $842.10. C. $861.00. D. $4,210.50.

B. $842.10.

If 95.44% of all outcomes are within two standard deviations above and below the mean and 2.15% of all outcomes are between two and three standard deviations above and 2.15% of all outcomes are between two and three standard below the mean, the percentage of all outcomes that lie beyond three standard deviations from (above and below) the mean is Select one: A. .13. B. .26. C. 2.15. D. 4.30.

B. .26. 100% - 95.44% - 2.15% - 2.15% =.26%; .26% of all outcomes lie outside three standard deviations above and below the mean.

If in calculating the mean, the outcomes are 2, 2, 5, 5, and 6, the mean is Select one: A. 3. B. 4. C. 5. D. 8.

B. 4

Assuming a normal distribution, 34.13% of all outcomes are within one standard deviation above the mean. If the portion of the distribution between one and two standard deviations above the mean contains 13.59% of all outcomes, what percentage is contained in the area between the mean and two standard deviations below the mean? Select one: A. 20.54% B. 47.72% C. 52.28% D. 68.26%

B. 47.72% 47.72% is contained in the area between the mean and two standard deviations below the mean. The area between the mean and two standard deviations above the mean contains 47.72% (34.13 + 13.59) of the outcomes, and since every normal distribution is symmetrical, another 47.72% of all the outcomes fall within the area between the mean and two standard deviations below the mean.

One way of jointly considering frequency and severity is to combine both frequency and severity distributions into Select one: A. A cumulative occurrence distribution. B. A total claims distribution. C. An asymmetrical probability distribution. D. A continuous and theoretical probability distribution

B. A total claims distribution.

In using the coefficient of variation when comparing two distributions, if both distributions have the same mean, then the distribution with the larger standard deviation will have Select one: A. Less variability. B. Greater variability. C. More skew. D. Less skew.

B. Greater variability.

Risk professionals use measures of dispersion of the distributions of potential outcomes to gain a better understanding of loss exposures being analyzed. Which one of the following is true regarding the standard deviation of a distribution? Select one: A. It is the average value of predicted losses estimated from an empirical distribution. B. It indicates how widely dispersed the values in a distribution are. C. It can only be calculated when the probability of each outcome in a sample of data is known. D. It is the probability of each possible outcome in a sample of data.

B. It indicates how widely dispersed the values in a distribution are.

Which one of the following best describes a probability distribution? Select one: A. It is a table, chart or graph that shows how many of each type of identified loss will occur during the next 12-month period. B. It represents probability estimates for a particular set of circumstances and the probability of each possible outcome. C. It shows the likelihood of particular future events and an estimate of the financial consequences of each predicted event. D. It predicts future events based on the frequency and severity of past events.

B. It represents probability estimates for a particular set of circumstances and the probability of each possible outcome.

In loss analysis, the Prouty Approach primarily involves Select one: A. Total dollar loss values. B. Loss frequency and severity. C. Loss credibility. D. Loss timing.

B. Loss frequency and severity.

Lucy is a commercial underwriter who is comparing two accounts to determine to which to offer coverage. The mean loss value on each account is roughly the same, and Lucy determines that the two accounts exhibit similar underwriting characteristics. All else being equal, Lucy would be best advised to select the account with Select one: A. Fewer data points. B. Lower standard deviation. C. Higher standard deviation. D. Higher coefficient of variation.

B. Lower standard deviation.

The table below represents the probability distribution of auto physical damage losses for a fleet of insured vehicles. Which one of the following statements is correct with respect to the information it provides? size of loss # of losses % of # of losses $0-$5k 8 40% $5,001-$10k 7 35% $10,001-$15k 2 10% $15,001-$20k 2 10% $20,001 + 1 5% total 20 100% Select one: A. There is a 30 percent probability of any loss being $5,000 or less. B. Maintaining a $5,000 deductible would eliminate 40 percent of the losses. C. This represents a theoretical probability distribution. D. This represents a discrete probability distribution.

B. Maintaining a $5,000 deductible would eliminate 40 percent of the losses.

Which one of the following statements regarding probability is correct? Select one: A. The probability of an event that is absolutely certain is 0. B. Probabilities associated with events such as coin tosses can be developed from theoretical considerations and are unchanging. C. Risk management professionals use theoretical probabilities because they are generally available for and applicable to claim analysis. D. The accuracy of theoretical probabilities depends on the size and representative nature of the samples being studied.

B. Probabilities associated with events such as coin tosses can be developed from theoretical considerations and are unchanging.

The mean is calculated by weighting each observed outcome by the Select one: A. Credibility factor. B. Relative frequency with which it occurs. C. Dollar value of the outcome. D. Adjusted modification factor.

B. Relative frequency with which it occurs.

The relationships among the mean, median, and mode for any data set are illustrated by the distribution's Select one: A. Density. B. Shape. C. Size. D. Variables.

B. Shape.

Which one of the following statements is true regarding central tendency when comparing the characteristics of probability distributions? Select one: A. The most widely accepted ways of measuring central tendency are referred to as the average, the weighted average, and the mean. B. The measures of central tendency represent the best guess as to what the outcome will be. C. The central tendency is the one single outcome that occurs most frequently. D. Most probability distributions cluster around the exact center of the distribution's range of values.

B. The measures of central tendency represent the best guess as to what the outcome will be.

Which one of the following statements is correct with respect to empirical probability distributions? Select one: A. Any given event can fall into one or more categories of event (bins). B. They provide a mutually exclusive, collectively exhaustive list of outcomes. C. Event categories (bins) are designed so that only the most probable events are included. D. The sum of all empirical probabilities in a distribution can be any number.

B. They provide a mutually exclusive, collectively exhaustive list of outcomes.

Investment income and interest earnings should be considered when analyzing which one of the following dimensions of loss exposures? Select one: A. Loss severity B. Timing C. Total loss dollars D. Loss frequency

B. Timing Investment income and interest earnings should be considered when analyzing the timing dimension of loss exposures.

In Fred's large landscaping business, he knows that there is a point where equipment becomes unsafe and difficult to maintain. Fred realizes that after 2,000 miles of use, his costs for maintenance on his large mowers and sod busters dramatically rise. Using probability analysis Fred can better know Select one: A. What type of equipment is needed for future projects. B. When to replace equipment. C. Which equipment is likely to cause bodily injury to operators or customers. D. When to schedule routine maintenance.

B. When to replace equipment. Correct. Using probability analysis Fred can better know when to replace equipment.

Risk professionals may be able to use measures of dispersion around estimated losses to determine Select one: A. The standard deviation. B. Whether to offer insurance coverage to a potential insured. C. The likelihood of specific types of losses. D. What premium to charge for a particular coverage.

B. Whether to offer insurance coverage to a potential insured.

Probability analysis would be most reliable for projecting losses in an organization Select one: A. That has recently expanded its operations. B. With a substantial volume of data on past losses. C. With a low number of historical losses. D. Planning to restructure its operations.

B. With a substantial volume of data on past losses.

Eric's tire business is operated out of a single warehouse. He has tires, equipment, furniture, and supplies at this location. Eric employs 15 individuals at a total cost of $50,000 monthly. The building is valued at $100,000, and the tires and equipment are worth $50,000. The supplies and furniture in the warehouse are worth approximately $5,000. If Eric's property is destroyed and not restored for an entire month, what is the maximum possible loss of that property? Select one: A. $100,000 B. $150,000 C. $155,000 D. $205,000

C. $155,000

An organization's premises and operations liability losses have a severity distribution with a mean of $10,000 and a standard deviation of $15,000. What is the coefficient of variation for this distribution? Select one: A. .60 B. .67 C. 1.5 D. 1.67

C. 1.5

An insurer is beginning to write business in a new state. The claim manager, Carla, wants to know how many new claim representatives to hire to accommodate the additional volume of claims. Based on the marketing department's estimate and industry data, Carla has determined the mean number of new claims to be 2,000, with a standard deviation of 1,000 in a normal distribution. If a claim representative can typically adjust 600 claims per year, and Carla wants at least 80 percent certainty that she has enough representatives, which one of the following represents how many representatives she will need to hire? Select one: A. 2 B. 3 C. 5 D. 6

C. 5 Carla's 80 percent certainty will fit within one standard deviation above the mean since 84.13% of all outcomes fall below one standard deviation above the mean. The number of new claims will then be 3,000, and since one claim manager can adjust 600 claims in a year, 5 additional representatives can handle the volume (3,000/600).

Underwriter Carl is choosing between account A and account B which both have the same expected loss, but account B has more variation in its possible loss outcomes. Carl will most likely choose account Select one: A. B because the standard deviation is smaller. B. A because the standard deviation is smaller. C. A because there is less risk involved in the loss exposure. D. B because there is less risk involved in the loss exposure.

C. A because there is less risk involved in the loss exposure.

Data credibility refers to the level of confidence that Select one: A. Past loss data was properly recorded. B. Losses that have not occurred in the past will not occur in the future. C. Available data can accurately indicate future losses. D. The statistical analysis of the four loss exposure dimensions was completed correctly.

C. Available data can accurately indicate future losses.

Which one of the following describes the distribution shape in which the mean, median, and mode all have the same value? Select one: A. Skewed left B. Asymmetrical C. Bell-shaped D. Skewed right

C. Bell-shaped

Maria is a risk management professional trying to analyze workers compensation loss frequency by cause of loss. Which one of the following forms of probability distribution would be most appropriate for her to use? Select one: A. Theoretical B. Continuous C. Discrete D. Hypothetical

C. Discrete

Determining the probability that a certain event will occur can be an important part of exposure analysis in the risk management process. Which one of the following is the term used for probability that is developed based on actual experience? Select one: A. Bona fide probability B. Theoretical probability C. Empirical probability D. Material probability

C. Empirical probability

Which one of the following statements is correct with respect to the timing dimension in the analysis of loss exposures? Select one: A. The timing dimension refers to when losses actually occur rather than when they are ultimately paid. B. Liability losses tend to be paid more quickly after an occurrence than property losses. C. Money held in reserve to pay for a loss can earn interest until the actual payment is made. D. A delay between occurrence of a loss and its payment decreases uncertainty about the value of a loss.

C. Money held in reserve to pay for a loss can earn interest until the actual payment is made.

In a probability distribution, John noticed the dispersion affected the shape of the distribution. In the distribution he was reviewing, he noted that the shape was altered as the dispersion decreased. Typically, a less dispersed distribution will form a Select one: A. Bell-curved distribution. B. Less peaked distribution. C. More peaked distribution. D. Flat distribution.

C. More peaked distribution.

Which one of the following statements is correct with respect to continuous probability distributions? Select one: A. They are most effectively illustrated using tables and pie charts. B. There are a finite number of possible outcomes in a continuous probability distribution. C. One way of presenting a continuous probability distribution is to divide the distribution into a countable number of bins. D. They are typically used for loss frequency analysis rather than severity analysis.

C. One way of presenting a continuous probability distribution is to divide the distribution into a countable number of bins.

Which one of the following types of data organization is the foundation for developing loss severity distributions or loss trends over time? Select one: A. Organizing losses by type of asset exposed B. Organizing losses by cause of loss C. Organizing losses by size D. Organizing losses historically by date

C. Organizing losses by size

Under The Prouty Approach of analyzing loss exposures, the four broad categories of loss frequency and the three loss severity categories are Select one: A. Quantitative. B. Narrowly defined. C. Subjective. D. Diversified.

C. Subjective.

When considering an empirical distribution, the measure of central tendency is called the mean. Which one of the following is correct with respect to the mean? Select one: A. The mean is the best estimate of expected outcomes because it is unaffected by changes in underlying conditions over time. B. The mean is the value at the midpoint of a sequential data set with an odd number of values. C. The mean is the sum of the values in a data set divided by the number of values. D. A risk professional will rarely use the mean to forecast future events.

C. The mean is the sum of the values in a data set divided by the number of values.

In a normal distribution 34.13% of all outcomes are within one standard deviation above the mean. The portion between one and two standard deviations above the mean contains 13.59% of all outcomes. What percentage of the total outcomes is between two standard deviations below the mean and two standard deviations above? Select one: A. 20.54% B. 47.72% C. 68.26% D. 95.44%

D. 95.44% The percentage of the total outcomes between two standard deviations below the mean and two standard deviations above 95.44%. The area between the mean and two standard deviations above the mean contains 47.72% (34.13 + 13.59) of the outcomes, and since every normal distribution is symmetrical, another 47.72% of all the outcomes fall within the area between the mean and two standard deviations below the mean. 47.72 + 47.72 = 95.44.

The normal distribution is a probability distribution that, when graphed, generates a particular type of curve. Which one of the following best describes that curve? Select one: A. Skewed either right or left B. Wide and flat C. Narrow and peaked D. Bell-shaped

D. Bell-shaped

In theory, liability losses are limited only by the Select one: A. Amount of insurance carried. B. Court's subjectivity. C. State's tort liability laws. D. Defendant's total wealth.

D. Defendant's total wealth.

Which one of the following is the term used for the weighted average of all the possible outcomes in a theoretical probability distribution? Select one: A. Mean B. Hypothetical norm C. Relative average D. Expected value

D. Expected value

An empirical probability distribution is based on Select one: A. Scientific principle. B. Theory. C. Logic. D. Historical data.

D. Historical data.

Which one of the following statements is true regarding typical shapes of symmetrical and skewed distributions? Select one: A. Many loss distributions are skewed because the probability of large losses is large and the probability of small losses is small. B. If the distribution is skewed, the mean and median value will be the same as the mode value. C. In a standard bell-shaped distribution, the mode has a greater value that either the mean or the median. D. In a symmetrical distribution, the mean and median have the same value.

D. In a symmetrical distribution, the mean and median have the same value.

In a normal distribution, fewer than 5% of outcomes are Select one: A. Within one standard deviation above or below the mean. B. Between the mean and two standard deviations above or below the mean. C. Between one and two standard deviations above or below the mean. D. Outside two standard deviations above or below the mean.

D. Outside two standard deviations above or below the mean.

To accurately analyze loss exposures using data on past losses, the data should meet certain criteria. Which one of the following lists those criteria? Select one: A. The data should be detailed, ample, and accurate. B. The data should be structured, numerical, indexed, and comprehensive. C. The data should be exhaustive, precise, and adjusted for inflation. D. The data should be relevant, complete, consistent, and organized.

D. The data should be relevant, complete, consistent, and organized.

see graph on bottom page 3.9 This graph illustrates a probability distribution. The horizontal axis illustrates possible outcomes, and the vertical axis shows the probability of each. Which one of the following statements is true regarding the information presented in this graph? Select one: A. It represents a continuous probability distribution. B. The most frequently occurring value is .17.Incorrect. The most frequently occurring value is seven. C. The sum of the estimated probabilities for all possible values is 78. D. The most frequently occurring value is seven.

D. The most frequently occurring value is seven.

One of the ways in which probabilities can be developed is theoretically. Which one of the following is an example of an event for which probability can be determined theoretically? Select one: A. The number of products liability lawsuits that can occur over a particular period of time B. The number of automobile accidents that can be expected in the upcoming year C. The number of 60-year-old men expected to die in a particular year D. The number of times heads can be expected to turn up over multiple coin tosses

D. The number of times heads can be expected to turn up over multiple coin tosses

Knowledge Check What type of probability distribution do risk managers typically utilize? Theoretical Empirical Mutually exclusive Collectively exhaustive

Empirical

When analyzing current property loss exposures based on historical data, the past loss data must be relevant to the current or future loss exposures. Which of the following valuation data would be relevant to the analysis? Repair or replacement cost at the time of restoration Original cost of the property Book value of the property at the time of loss Anticipated future value of the property

Repair or replacement cost at the time of restoration

categories of loss severity in the Prouty approach are

Slight -Organization can readily retain each loss exposure. Significant -Organization cannot retain the loss exposure, some part of which must be financed. Severe - Organization must finance virtually all of the loss exposure or endanger its survival.

Probability analysis is a technique for forecasting events on the assumption that they are governed by an unchanging probability distribution. True False

True

discrete probability distributions have

a finite number of possible outcomes

law of large numbers

a mathemeatical principle stating that as the number of similar but independent exposure units increases, the relative accuracy of predictions about future outcomes (losses) also increase

standard deviation is

a measure of dispersion between the values in a distribution and the expected value (or mean) of that distribution, calculated by taking the square root of the variance

coefficient of variation is

a measure of dispersion calculated by dividing a distribution's standard deviation by its mean

probability distribution is

a presentation (table, chart, or graph) of probability estimates of a particular set of circumstances and of the probability of each possible outcome

normal distribution

a probability distribution that, when graphed, generates a bell-shaped curve

empirical probability is

a probability measure that is based on actual experience through historical data or from the observation of facts

probability analysis is

a technique for forecasting events, such as accidental and business losses, on the assumption that they are governed by an unchanging probability distribution

continuous probability distributions have

an infinite number of possible outcomes

Which one of the following statistical measures is used to assess the credibility of expected loss values? a Mode b Standard deviations c. Mean d. Average

b Standard deviations

Which one of the following statements concerning measures of central tendency is most accurate? a The mean is the best measure of central tendency even for distributions that have large outlier values b The mode of a distribution provides information on the outcomes that are the most common c The mode is defined as the midpoint of a sequential data set d With a skewed distribution, the mean and the median are always equal to one another

b The mode of a distribution provides information on the outcomes that are the most common

Which one of the following statements best describes the law of large numbers as it is applied in risk management? a The more property exposed to loss, the less predictable the future losses b The larger the set of numbers in a loss report, the greater the potential for rounding error when summarizing the data c As the number of similar but independent exposure units increases, the accuracy of predictions about future losses increases as well d Managers tend to be more concerned about the probability of frequent small losses than about the probability of a single large loss

c as the number of similar but independent exposure units increases, the accuracy of predictions about future losses increases as well

Which one of the following statements about the use of probability distributions in making risk management decisions is most accurate> a Insurance and risk management professionals primarily use theoretical distributions rather than empirical distributions to analyze potential losses b Continuous probability distributions have a finite number of potential outcomes, which makes them particularly useful for analyzing how often something will occur. c. Discrete probability distributions have a countable number of outcomes, and display all possible outcomes and the probability of each d Empirical probability distributions contain outcomes that are collectively exhaustive, but not necessarily mutually exclusive

c. Discrete probability distributions have a countable number of outcomes, and display all possible outcomes and the probability of each

Coefficient of variation is

calculated as a standard deviation divided by its mean and useful for comparing distributions with different means or standard deviations

Which one of the following statements concerning data requirements for loss exposure analysis is most accurate? a. The more years of loss data an organization has, the greater the likelihood that it continues to be relevant. b. Loss amounts should always be maintained on an original cost basis to avoid inflation distortion c. to ensure that the loss data is complete and consistent, only internal information provided by the insured organization should be used to evaluate potential losses d. loss data collected from different sources may be distorted when those different sources use different accounting methods to record the losses

d. loss data collected from different sources may be distorted when those different sources use different accounting methods to record the losses

forms of probability distribution are

discrete and continuous

MPL =

maximum possible loss

Loss exposure analysis is often based on

probability and statistical analysis of data

Theoretical probability

probability that is based on theoretical principles rather than on actual experience

to analyze current loss exposures on historical data, the past loss data must be

relevant to the current or future loss exposures

Obtaining complete data about past losses for particular loss exposures often requires

relying on others, both inside and outside the organization.

mean is

the average

median

the middle value, the mid point in a sequential data set

mode is

the most common amount

mode is

the most frequently occurring value in a distribution

Central tendency is

the single outcome that is the most representative of all possible outcomes included within a probability distribution

mean is

the sum of the values in a data set divided by the number of values

median is

the value at the midpoint of sequential data set with an odd number of values, or the mean of the two middle values of a sequential data set with an even number of values

dispersion is

the variation among values in a distribution

expected value is

the weighted average of all the possible outcomes of a probability distribution

Concepts affecting the basic nature of probability include

theoretical probability, empirical probability, and the law of large numbers.