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Suppose X and Y are independent random variables and that X~ on (2,5). Calculate the probability that 2X + Y < 8. Exp(14) and Y is uniformly distributed Proposed solution: Because X and Y are independent, the joint p.d.f. is given by the product of the p.d.f. of X and of Y,

Suppose X and Y are independent random variables and that X~ on (2,5). Calculate the probability that 2X + Y < 8. Exp(14) and Y is uniformly distributed Proposed solution: Because X and Y are independent, the joint p.d.f. is given by the product of the p.d.f. of X and of Y,

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Suppose X and Y are independent random variables and that X ~ Exp(14) and Y is uniformly distributed on (2,5). Calculate the probability that 2X + Y < 8. Proposed solution: Because X and Y are independent, the joint p.d.f. is given by the product of the p.d.f. of X and of Y, that is The desired probability is 10 r8-y P(2X + Y <8) To fo = fx,y(x, y) = = 3 e -14s dsdt -14x {fo-te x>0, y > 0 otherwise. 10 e-140 100 I 14 8-t dt = [- е 3 •10 14 14 ₁ (1 - e-14 (8-1)dt = 1/2 [ 1 - 11e-14(8-1)] 10 3 4 = 28- 1 -56 -(e- 14 - e-28).
Transcribed Image Text:Suppose X and Y are independent random variables and that X ~ Exp(14) and Y is uniformly distributed on (2,5). Calculate the probability that 2X + Y < 8. Proposed solution: Because X and Y are independent, the joint p.d.f. is given by the product of the p.d.f. of X and of Y, that is The desired probability is 10 r8-y P(2X + Y <8) To fo = fx,y(x, y) = = 3 e -14s dsdt -14x {fo-te x>0, y > 0 otherwise. 10 e-140 100 I 14 8-t dt = [- е 3 •10 14 14 ₁ (1 - e-14 (8-1)dt = 1/2 [ 1 - 11e-14(8-1)] 10 3 4 = 28- 1 -56 -(e- 14 - e-28).
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