ELEMENTARY STATISTICS BLUMAN Discrete Probability Distribution 2019 Mc

ELEMENTARY STATISTICS, BLUMAN Discrete Probability Distribution © 2019 Mc. Graw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of Mc. Graw-Hill Education.

Objectives for this Power. Point In this Power. Point we will learn how to construct a discrete probability distribution. © 2019 Mc. Graw-Hill Education

Definition 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. It is basically a table with the values of the random variable and their associated probabilities. If a graph is required, place the outcomes on the x axis and the probabilities on the y axis, and draw vertical bars for each outcome and its corresponding probability. © 2019 Mc. Graw-Hill Education

Example In a family with three children, the possible outcomes with regard to gender are 3 boys. Another possibility is two boys, and one girl, where the girl is the youngest, the middle child, or the oldest. Another possibility is one boy and two girls where the boy is the oldest, the middle child, or the youngest. The last possibility is 3 girls. The following represents the total possibilities: © 2019 Mc. Graw-Hill Education BBB BGG BBG GBG BGB GBB GGG

Identify Random Variable We need to identify our random variable. In this case, we will let x equal the number of girls in a family with three children. BBB BGG BBG GBG BGB GBB GGG From our sample space, we can see that the probability that this family would have 0 girls is 1/8 (BBB). The probability that there would be 1 girl is 3/8 (BBG, BGB, GBB). The probability that there would be two girls is 3/8 (BGG, GBG, GGB) and the probability that there would be 3 girls is 1/8 (GGG). © 2019 Mc. Graw-Hill Education

Discrete Probability Distribution x 0 1 2 3 P(x) 1/8 3/8 1/8 © 2019 Mc. Graw-Hill Education

Two Requirements for a Probability Distribution 1. The sum of the probabilities of all events in the sample space must equal 1. 2. The probability of each event in the sample space must be between or equal to 0 and 1. Example: Determine whether each distribution is a probability distribution: X 2 4 6 8 10 P(X) 0. 3 0. 4 0. 1 0. 2 0. 1 Answer: No. The sum of the probabilities is greater than 1. © 2019 Mc. Graw-Hill Education

Exercise Determine whether each distribution is a probability distribution: X 3 7 10 12 P(X) -0. 6 0. 3 0. 2 Solution: No. Why? X BB BG GB GG P(X) 1/4 1/4 Solution: Yes. Why? © 2019 Mc. Graw-Hill Education