Outline of Chapter 5 text - Elementary Statistics: A Brief Version(A. Bluman 3rd Ed., 2003)
Chapter 5 Outline
Construct a probability distribution for a random variable.
Find the mean, variance, and expected value for a discrete random variable.
Find the exact probability for X successes in n trials of a binomial experiment.
Find the mean, variance, and standard deviation for the variable of a binomial distribution.
Find probabilities for outcomes of variables using the Poisson, hypergeometric, and multinomial distributions.
Many decisions in business, insurance, and other real-life situations are made by assigning probabilities to all possible outcomes pertaining to the situation and then evaluating the results.
This chapter explains the concepts and applications of probability distributions. In addition, special probability distributions, such as the binomial, multinomial, Poisson, and hypergeometric distributions are explained.
A random variable is a variable whose values are determined by chance.
Discrete Probability Distribution
A discrete probability distribution consists of the values a random variable can assume and the corresponding probabilities of the values. The probabilities are determined theoretically or by observation.
Calculating the Mean
In order to find the mean for a probability distribution, one must multiply each possible outcome by its corresponding probability and find the sum of the products.
The mean, variance, and standard deviation should be rounded to one more decimal place than the outcome, X.
Variance of a Probability Distribution
The variance of a probability distribution is found by multiplying the square of each outcome by its corresponding probability, summing those products, and subtracting the square of the mean.
The formula for calculating the variance is:
The formula for the standard deviation is:
Expected value or expectation is used in various types of games of chance, in insurance, and in other areas, such as decision theory.
Expected Value (cont'd.)
The expected value of a discrete...
... a discrete distribution. Characteristics of a Binomial Distribution There must be a fixed number of trials. The outcome of each trial must be independent. Each experiment can have only two outcomes or be reduced to two outcomes. The probability of ...
... for variances and standard deviations. The chi-square distribution is obtained from the values of (n-1)s2/s 2 when random samples are selected from a normally distributed population whose variance is ...
... the variable is normally distributed, the sample standard deviation is used, but a t test should be conducted if the sample size is less than 30. Summary (cont'd.) Researchers compute a test value from ...
... actual experience to determine the likelihood of outcomes. Given a frequency distribution, the probability of an event being in a given class is: Subjective Probability Subjective probability uses a probability value based ...
... normally distributed, and the standard deviations of the variable must ... means using the z test. Test the difference between two variances or standard deviations. Objectives (cont'd.) Test the difference between two means for small independent ...
... data value or a datum. Random variables have values that are determined by chance. Insurance companies set their rates based on random variables. Over ...
... a variable. Variance and Standard Deviation (cont'd.) The variance and standard deviation are used to determine the number of data values that fall within a specified interval in a distribution. The variance and standard deviation are ...
... normal distribution with mean and standard deviation As the sampling distribution of ... Conditional Probabilities Objective: To find out whether the probability that ... we were unable to calculate the correlations between the different variables, which would have given us more interesting insights into the ...