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2. When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and each headlight is checked to see whether it is properly aimed. Let X denote the number of headlights that need adjustment, and let Y denote the number of defective tires. a. If X and Y are independent with p(0) = .5, A(1) = .3. Po(2) = 2, and p,(0) = .6, p(1) = .1. py(2) = p;(3) = .05, and p,(4) = .2, display the joint pmf of (x, ) in a joint probability table. b. Compute P(Xs1 and Ys 1) from the joint probability table, and verify that it equals the product P(X= 1)· P(Y< 1). c. What is P(X+ Y = 0) (the probability of no violations)? d. Compute P(X + Y< 1).

2. When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and each headlight is checked to see whether it is properly aimed. Let X denote the number of headlights that need adjustment, and let Y denote the number of defective tires. a. If X and Y are independent with p(0) = .5, A(1) = .3. Po(2) = 2, and p,(0) = .6, p(1) = .1. py(2) = p;(3) = .05, and p,(4) = .2, display the joint pmf of (x, ) in a joint probability table. b. Compute P(Xs1 and Ys 1) from the joint probability table, and verify that it equals the product P(X= 1)· P(Y< 1). c. What is P(X+ Y = 0) (the probability of no violations)? d. Compute P(X + Y< 1).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2. When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and each headlight is checked to see whether it is properly aimed. Let X denote the number of headlights that need adjustment, and let Ydenote the number of defective tires. a. If X and Y are independent with p(0) = .5, p(1) = .3, Px{2) = .2, and p;(0) = .6. p(1) = .1. P;{2) = p;(3) = .05, and p,(4) = .2, display the joint pmf of (X, Y) in a joint probability table. b. Compute P(Xsl and Y< 1) from the joint probability table, and verify that it equals the product P(X<1)· P(Y< 1). c. What is P(X+ Y= 0) (the probability of no violations)? d. Compute P(X+ Y< 1).
Transcribed Image Text:2. When an automobile is stopped by a roving safety patrol, each tire is checked for tire wear, and each headlight is checked to see whether it is properly aimed. Let X denote the number of headlights that need adjustment, and let Ydenote the number of defective tires. a. If X and Y are independent with p(0) = .5, p(1) = .3, Px{2) = .2, and p;(0) = .6. p(1) = .1. P;{2) = p;(3) = .05, and p,(4) = .2, display the joint pmf of (X, Y) in a joint probability table. b. Compute P(Xsl and Y< 1) from the joint probability table, and verify that it equals the product P(X<1)· P(Y< 1). c. What is P(X+ Y= 0) (the probability of no violations)? d. Compute P(X+ Y< 1).
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