Introduction to Probability Distributions Skill 23 a Objectives

Introduction to Probability Distributions Skill 23 a

Objectives • Distinguish between different probability distributions. • Understand when to use different probability distributions.

Discrete Probability Distribution A discrete probability distribution is an assignment of probabilities to each distinct value of a discrete random variable or to each interval of values of a continuous random variable. 1) Has a probability assigned to each distinct value of the random variable. 2) The sum of all assigned probabilities must be 1. 3) The mean is called the expected value of the distribution. 4) The standard deviation is called the measure of risk.

Binomial Probability Distribution A binomial probability distribution is sometimes called a Bernoulli Experiment. This distribution is common when we are interested in exactly two possible outcomes for each trial of interest. 1) Each trial must be independent of each other 2) Each trial is either success or failure. 3) Experiment has a certain number of desired successes, r. 4) The probability of success, p, is always the same. 5) The question asked: “Find the probability of r successes out of n trials. ”

Geometric Probability Distribution A geometric probability distribution is a binomial experiment in which we repeat as many trials as we need until we get our first success. 1) Has a given number of trials before success. We call this n. 2) Each trial is independent of each other. 3) The probability of success, p, is always the same. 4) The question asked: “Find the probability of the first success happening on the nth trial. ”

Poisson Probability Distribution A Poisson probability distribution as the number of trials gets larger, the probability of success gets smaller. This distribution estimates the probability of success in a given interval. 1) Has two outcomes. 2) Each event is independent of each other. 3) The desired number of successes, we call, r. 4) The question asked: “Find the probability of getting r successes in the interval. ”

Normal Probability Distribution A normal probability distribution also called the Gaussian Distribution. The results of a normal distribution center around the mean and get less frequent as we move away from the mean. Usually represented with a normal curve. 1) Curve is bell-shaped with highest value around mean. 2) Curve is symmetrical around mean. 3) Curve approaches but never crosses the horizontal axis. 4) The area under the curve has the sum of 1. 5) Used to estimate many things; tests scores, economics, heights, ect.

Chi-Square Probability Distribution A Chi-Square probability distribution similar to the normal distribution, however, it is skewed in some way and is not symmetric around the mean. Instead the mode is the high point. 1) The area under the curve is 1. 2) Need to find the degrees of freedom, d. f. 3) Used to find goodness of fit. 4) Used when we do not know if a distribution is normal, this can “normalize” the distribution.

23 a; Introduction to Probability Distributions � Summarize � Homework ◦ Worksheet Notes