Chapter 5 - 6
EVENT
A collection of one or more outcomes of an experiment.
General Rule of Multiplication
If two events are not independent, they are referred to as dependent.
Probability of 0
Represents something that cannot happen.
General Rule of Addition and Joint Probability
The likelihood that two events both happen. When two possible outcomes occur, add the non-duplicated outcomes and subtract the duplicated outcomes. P(A or B) = P(A) + P(B) - P(A and B)
INDEPENDENCE
The occurrence of one event has no effect on the probability of the occurrence of another event.
Bayes' Theorem
A formula used to derive the probability that something exists.
Correlation is:
A mutual relation between two or more things. Remember: causation causes correlation. The reverse is not necessarily true (correlation does not prove causation). A concept from statistics that measures the relationship between two things.
OUTCOME
A particular result of an experiment.
Positive / Negative Correlation
A positive correlation means that when one thing goes up, the other goes too. A negative correlation is the opposite, when one goes up, the other goes down.
JOINT PROBABILITY
A probability that measures the likelihood two or more events will happen concurrently.
EXPERIMENT
A process that leads to the occurrence of one and only one of several possible observations. An experiment has two or more possible outcomes and it is uncertain which one will occur.
Emotive Bias
Another reason behind correlation and causation errors. Hoping to find a link that would support an agenda. Allowing emotions to cloud judgment.
PERMUTATION
Any arrangement of r objects selected from a single group of n possible objects. Permutation (P) equals the total number of objects factored (n-factor) or (n!) divided by the factor of the total number of objects (n) less the number objects selected (r) P = n! / (n-r)!
COLLECTIVELY EXHAUSTIVE
At least one of the events must occur when an experiment is conducted. Example: For a die-tossing experiment, every outcome will be either even or odd. So the set is collectively exhaustive.
Special Rule of Multiplication
For two independent events A and B, the probability that A and B will both occur is found by multiplying the two probabilities. P(A and B) = P(A)P(B)
Combination Formula
If the order of the selected objects is not important, any selection is called a combination. Combination (C) equals the total number of objects factored (n!) divided by the product of the factor of items selected (r!) and the factor of the total number less the number of those selected. C = n! / r!(n-r)!
MULTIPLICATION FORMULA
If there are m ways of doing one thing and n ways of doing another thing, there are m x n ways of doing both. Total number of arrangements = (m)(n)
Descriptive statistics
Is concerned with summarizing data collected from past events.
Probability of 1
Represents something that is certain to happen. If the set of events is collectively exhaustive and the events are mutually exclusive, the sum of the probabilities is 1
Complement Rule of Addition
The probability of occurrence plus the probability of non-occurrence must equal 1. P(A) + P(-A) = 1 or P(A) = 1 - P(-A) Used to determine the probability of an event occurring by subtracting the probability of the event not occurring from 1. Sometimes it is easier to calculate the probability of an event happening by determining the probability of it not happening and subtracting the result from 1
EMPIRICAL PROBABILITY or Relative Liability
The second type of objective probability. Based on relative frequencies. The probability of an event happening is the fraction of the time similar events happened in the past. EP = Number of times and event occurs divided by the total number of observations. Based on the law of large numbers - more observations increases accuracy of estimate of probability.
Objective and Subjective Viewpoint (Probability)
Two approaches to assigning probabilities to an event.
Probability Theory
A value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur. The science of uncertainty. Allows the decision maker with only limited information to analyze the risks and minimize the gamble inherent.
Descriptive statistics. Chapter 1-4.
Chapter 2 - organize profit data into a frequency distribution. Chapter 3 - use numerical measures of location and dispersion, such as range and standard deviation, to locate a typical profit on vehicle sales and to examine the variation in the profit of a sale. Chapter 4 - develop charts and graphs, such as a scatter diagram, to further describe the data graphically.
Causality
Is the area of statistics that is most commonly misused, and misinterpreted, by non-specialists.
Causation is:
A relationship in which one action or event is the direct consequence of another
POSTERIOR PROBABILITY
A revised probability based on additional information.
Contingency Tables
A two-way table and use the results of this tally to determine various probabilities.
Special Rule of Addition
Events must be mutually exclusive - if one event occurs not of the other events can occur. For two mutually exclusive events: P(A or B) = P(A) + P(B) For three mutually exclusive events: P(A or B or C) = P(A) + P(B) + P(C)
Subjective Probability
If there is little or no experience or information on which to base a probability, it may be arrived at subjectively. Essentially, this means an individual evaluates the available opinions and information and then estimates or assigns the probability
Probability
Is frequently expressed as a decimal, such as .70, .27, or .50. It can assume any number from 0 to 1, inclusive. Even a fraction.
Objective Probability
Objective probability is subdivided into (1) classical probability and (2) empirical probability. Probability of an event equals the number of favorable outcomes divided by the total number of probable outcomes. Example: 111 trouble free plane flights divided by 113 total plane flights equals .98 percent probability of a trouble free plane flight.
LAW OF LARGE NUMBERS
Over a large number of trials, the empirical probability of an event will approach its true probability. Example: Flipping fair coin at first may not but over a larger number of observations will approach probability of 1.5. Based on the empirical or relative frequency approach to probability, the probability of the event happening approaches the same value based on the classical definition of probability
SUBJECTIVE CONCEPT OF PROBABILITY
The likelihood (probability) of a particular event happening that is assigned by an individual based on whatever information is available. Example: 1. Estimating the likelihood the New England Patriots will play in the Super Bowl next year. 2. Estimating the likelihood you will be married before the age of 30. 3. Estimating the likelihood the U.S. budget deficit will be reduced by half in the next 10 years.
2 Rules of multiplication.
The likelihood that two events both happen. Special Rule General Rule
MUTUALLY EXCLUSIVE
The occurrence of one event means that none of the other events can occur at the same time. Example: Gender creates 2 mutually exclusive outcomes.
Classical Approach
The first type of objective probability. Based on equally likely outcomes. If the set of events is collectively exhaustive and the events are mutually exclusive, the sum of the probabilities is 1. It is unnecessary to do an experiment to determine the prob- ability of an event occurring using the classical approach because the total number of outcomes is known before the experiment. Example: Given that 1,000 possible outcomes exist (000 through 999), the probability of winning with any three-digit number is 0.001, or 1 in 1,000.
PRIOR PROBABILITY
The initial probability based on the present level of information.
Statistical inference or Inferential Statistics. Chapter 5
Second facet of statistics, namely, computing the chance that something will occur in the future. Deals with conclusions about a population based on a sam- ple taken from that population.
2 Rules of Addition
Special Rule Complement Rule
CONDITIONAL PROBABILITY
The probability of a particular event occurring, given that another event has occurred. The general rule of multiplication states that for two events, A and B, the joint probability that both events will happen is found by multiplying the probability that event A will happen by the conditional probability of event B occurring given that A has occurred. P(A and B) = P(A)P(B ƒ A)
