# Chap 5 - Chapter 5 Discrete Probability Distributions...

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 5 Discrete Probability Distributions Learning Objectives 1. Understand the concepts of a random variable and a probability distribution. 2. Be able to distinguish between discrete and continuous random variables. 3. Be able to compute and interpret the expected value, variance, and standard deviation for a discrete random variable. 4. Be able to compute and work with probabilities involving a binomial probability distribution. 5. Be able to compute and work with probabilities involving a Poisson probability distribution. 6. Know when and how to use the hypergeometric probability distribution. Solutions: 5 - 1 Chapter 5 1. a. Head, Head (H,H) Head, Tail (H,T) Tail, Head (T,H) Tail, Tail (T,T) b. x = number of heads on two coin tosses c. Outcome Values of x (H,H) 2 (H,T) 1 (T,H) 1 (T,T) d. Discrete. It may assume 3 values: 0, 1, and 2. 2. a. Let x = time (in minutes) to assemble the product. b. It may assume any positive value: x > 0. c. Continuous 3. Let Y = position is offered N = position is not offered a. S = {(Y,Y,Y), (Y,Y,N), (Y,N,Y), (Y,N,N), (N,Y,Y), (N,Y,N), (N,N,Y), (N,N,N)} b. Let N = number of offers made; N is a discrete random variable. c. Experimental Outcome (Y,Y,Y) (Y,Y,N) (Y,N,Y) (Y,N,N) (N,Y,Y) (N,Y,N) (N,N,Y) (N,N,N) Value of N 3 2 2 1 2 1 1 4. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 5. a. S = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3)} b. Experimental Outcome (1,1) (1,2) (1,3) (2,1) (2,2) (2,3) Number of Steps Required 2 3 4 3 4 5 6. a. values: 0,1,2,...,20 discrete b. values: 0,1,2,... discrete c. values: 0,1,2,...,50 discrete d. values: 0 ≤ x ≤ 8 continuous e. values: x > 5 - 2 Discrete Probability Distributions continuous 7. a. f ( x ) ≥ 0 for all values of x . Σ f ( x ) = 1 Therefore, it is a proper probability distribution. b. Probability x = 30 is f (30) = .25 c. Probability x ≤ 25 is f (20) + f (25) = .20 + .15 = .35 d. Probability x > 30 is f (35) = .40 8. a. x f ( x ) 1 3/20 = .15 2 5/20 = .25 3 8/20 = .40 4 4/20 = .20 Total 1.00 b. c. f ( x ) ≥ 0 for x = 1,2,3,4. Σ f ( x ) = 1 9. a. Age Number of Children f ( x ) 6 37,369 0.018 7 87,436 0.043 8 160,840 0.080 9 239,719 0.119 5 - 3 .1 .2 .3 .4 f ( x ) x 1 2 3 4 Chapter 5 10 286,719 0.142 11 306,533 0.152 12 310,787 0.154 13 302,604 0.150 14 289,168 0.143 2,021,175 1.001 b. c. f ( x ) ≥ 0 for every x Σ f ( x ) = 1 Note: Σ f ( x ) = 1.001 in part (a); difference from 1 is due to rounding values of f ( x ). 10. a. x f ( x ) 1 0.05 2 0.09 3 0.03 4 0.42 5 0.41 1.00 b. x f ( x ) 1 0.04 2 0.10 3 0.12 4 0.46 5 0.28 1.00 5 - 4 6 7 8 9 10 11 12 13 14 .02 .04 .06 .08 .10 .12 .14 .16 f ( x ) x Discrete Probability Distributions c. P (4 or 5) = f (4) + f (5) = 0.42 + 0.41 = 0.83 d. Probability of very satisfied: 0.28 e. Senior executives appear to be more satisfied than middle managers. 83% of senior executives have a score of 4 or 5 with 41% reporting a 5. Only 28% of middle managers report being very satisfied....
View Full Document

## This note was uploaded on 11/08/2011 for the course MAT/FIN 272 taught by Professor Burns during the Spring '11 term at Central Connecticut State University.

### Page1 / 25

Chap 5 - Chapter 5 Discrete Probability Distributions...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online