ARM 401 Chapter 3 - Part 1

These probabilities may change as:

New data is discovered, or the environment that produces those events changes.

When outcomes are mutually exclusive, it means that:

No more than one of them can occur at a time.

A properly constructed probability distribution always contains:

Outcomes that are both mutually exclusive and collectively exhaustive.

Theoretical probabilities are based on:

Principles rather than actual experience.

Some of the additional benefits of a probability analysis or distribution, are:

Prioritizing loss exposures, by likelihood or potential severity, predicting and estimating both the positive and negative consequences of risk, and evaluating and prioritizing risk management decisions.

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

Probability analysis.

The outcomes in a continuous probability distribution are called:

Probability density functions.

A presentation, A K A a table, chart, or graph of probability estimates of a particular set of circumstances and of the probability of each possible outcome, is called:

Probability distribution.

This is an empirical probability because it's estimated by:

Studying the loss experience of men.

To be accurate, the samples under study must be:

Sufficiently large and representative.

When the two concepts are combined, you have what's called:

The M E C E. Mutually exclusive, collectively exhaustive principle.

Without that information, it's nearly impossible to determine:

The best course of action to take regarding that risk.

Continuous probability distributions are typically used for:

The consequences of an event.

The law of large numbers can be used to forecast future events based on past events only if:

The future events can be expected to occur under the same, unchanging conditions as those on which the predictions are based.

This illustrates:

The law of large numbers

This illustrates:

The law of large numbers.

A probability analysis predicts:

The likelihood of an event.

Risk professionals can use a probability analysis to predict:

The likelihood of an event.

Risk professionals need to be able to estimate:

The likelihood that a loss will occur, and the consequences if it does.

The probability of an event is:

The likelihood that it will happen over a period of time, assuming that the environment remains relatively unchanged.

The probability of an event is:

The likelihood that it will happen, or the frequency with which it will happen, over a specific period of time, assuming that the environment remains stable.

The larger the sample of past losses an organization can use in the analysis:

The more accurate the projections will be.

The probability distribution then predicts the likelihood that:

The outcome will land within one of the bins.

For example, from a description of a regular coin or die, a person who has never seen either can calculate:

The probability of flipping a heads or rolling a four.

An example of empirical probability is:

The probability that a male will die at age 68.

So by dividing the continuous distribution into a finite number of bins, a risk manager can calculate:

The probability that an outcome will fall within a certain range.

Empirical probabilities become more accurate as:

The sample size increases.

Continuous probability distributions depict:

The value of the loss or gain rather than the number of outcomes.

Probabilities can be developed from either:

Theoretical data distributions or historical data.

Although it may be preferable to use:

Theoretical probabilities because of their unchanging nature.

Other probability concepts risk professionals need to be familiar with, include:

Theoretical probabilities, empirical probabilities, and the law of large numbers.

Probability that is based on theoretical principles rather than on actual experience, is called:

Theoretical probability.

For example, on a particular coin flip, only one outcome is possible: heads or tails. Therefore:

These outcomes are mutually exclusive. Similarly, these two outcomes are the only possible outcomes and are therefore collectively exhaustive.

However, the law of large numbers is only relevant and accurate when forecasting future events that meet all of these criteria:

They occurred in the past under substantially identical conditions and resulted from unchanging forces. They can be expected to occur in the future under the same unchanging conditions. They have been and will continue to be both independent of one another and sufficiently numerous.

For example, the probability that a coin will land with its heads side facing up can be expressed as:

1/2, 50 percent, or 0.50.

The probability of a certain event is:

100%, or 1.0.

For example, in a discrete frequency distribution, the probability that no fires will occur in a high-rise office building may be 0.50. The probability that one fire will occur might be 0.35, and the chances of having two or more fires could be 0.15. If a fire occurs, the damage may cost between $0 and $100 million, which is: this type of probability distribution:

A continuous probability distribution.

There are multiple ways to represent:

A continuous probability distribution.

Discrete probability distributions, such as the hurricane exhibit, have:

A finite number of possible outcomes.

Any probability can be expressed as:

A fraction, percentage, or decimal.

The number of hurricanes making landfall in Florida is an example of:

A frequency distribution.

Another term for empirical probability is:

A posteriori probability.

Empirical probability is A K A:

A posteriori probability.

To do so, you should understand how to create and use:

A probability analysis and probability distribution.

Assigning a probability to the likelihood of having a loss amount of $35,456.32 would be nearly impossible. However, if the severity distribution is divided into a finite number of bins, such as $0-$1,000,000, $1,000,001-$2,000,000, and so on, then:

A probability can be assigned to each bin.

Empirical probability analysis is particularly effective for projecting the likelihood and consequences of losses or gains in organizations that have both:

A substantial volume of historical data, A K A experience, and fairly stable operations, so that loss and gain patterns will presumably continue unchanged.

Empirical probabilities, meanwhile, are based on:

Actual experience.

A probability distribution shows:

All of the possible outcomes of an event next to the likelihood of those outcomes.

Risk professionals can use a probability distribution to show:

All of the possible outcomes of an event next to the likelihood of those outcomes.

So to provide a mutually exclusive, collectively exhaustive list of outcomes, a distribution's categories A K A bins must be designed so that:

All outcomes can be included.

Discrete probability distributions are usually displayed in a table that lists:

All possible outcomes and the probability of each.

Such organizations may view past experience as:

An accurate sample of all possible losses or gains the organization might sustain in the future.

For certain types of probability distributions, like those dealing with an investment's possible gains or losses:

An infinite number of outcomes may be possible.

By definition, continuous probability distributions have this number of possible outcomes:

An infinite number of possible outcomes.

Whereas continuous probability distributions, such as the investment exhibit, have:

An infinite number of possible outcomes.

When outcomes are collectively exhaustive, it means that:

At least one of them will occur.

A properly constructed probability distribution always contains outcomes that are:

Both mutually exclusive and collectively exhaustive.

Therefore, you can't use Law of Large Numbers to predict the number of house fires on the west coast, if you aren't using:

Data from California homes that are potentially in the path of wildfires.

All probability distributions can be classified as either:

Discrete or continuous.

Probability distributions come in two forms:

Discrete probability distributions and continuous probability distributions.

As a result, these types of probabilities are often used for risk management applications:

Empirical probabilities.

Although risk managers occasionally analyze loss exposures using theoretical distributions, most of the work they do involves:

Empirical probability distributions.

A probability measure that is based on actual experience through historical data or from the observation of facts, is called:

Empirical probability.

One method is to divide the bins into:

Equal, standard sizes.

Empirical probabilities are only:

Estimates.

Theoretical probabilities aren't applicable or available in most of the situations that risk professionals are likely to analyze, such as:

Fires or workers compensation claims.

The law of large numbers also applies to:

Gains, and other outcomes.

Therefore, the probabilities of all events that are neither totally impossible nor absolutely certain are:

Greater than zero, but less than 100 percent or 1.0.

Empirical probability is associated with:

Historical data.

These distributions are typically used to analyze:

How often something will occur. That is, they are shown as frequency distributions.

A mathematical principle stating that as the number of similar but independent exposure units increases, the relative accuracy of predictions about future outcomes, A K A losses, also increases, is called:

Law of large numbers.

A mathematical principle stating that as the number of similar but independent exposure units increases, the relative accuracy of predictions about future outcomes, A KA losses also increases, is called:

Law of large numbers.

Theoretical probability is associated with events such as:

Coin tosses or dice throws.

Typically, events also have a range of:

Consequences, A K A severities, each with its own probability of occurring.

In contrast, theoretical probabilities are:

Constant, as long as the physical conditions that generate them, such as how many sides a die has, remain unchanged.

Theoretical probability is:

Unchanging.

The probability of an impossible event is:

Zero.