Answered: Let X be a continuous random variable…

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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$Problem 4.5 (Video 3.3, 3.4) Let X be a continuous random variable representing the (exact) lifetime of your TV set, measured in years. A simple model for X is that is an Exponential (A) random variable. You may assume that your brand of TV has an average lifetime of 20 years. 2 (a) What is the probability that the TV fails in the first year? (b) What is the probability that it lasts more than 5 years? (c) Consider the event B = {X ≥ 10} that your TV has already lasted 10 years. What is the conditional PDF ƒx\B(x)? (d) Let Y = X - 10. What is the conditional probability of Y given B = {X ≥ 10}? You can get this by simply transforming ƒx|ß(x) as fy|B(y) = fx|b(y +10). (e) Assume your TV has already lasted 10 years. What is the probability that it fails during the next year?$

Transcribed Image Text:Problem 4.5 (Video 3.3, 3.4) Let X be a continuous random variable representing the (exact) lifetime of your TV set, measured in years. A simple model for X is that is an Exponential (A) random variable. You may assume that your brand of TV has an average lifetime of 20 years. 2 (a) What is the probability that the TV fails in the first year? (b) What is the probability that it lasts more than 5 years? (c) Consider the event B = {X ≥ 10} that your TV has already lasted 10 years. What is the conditional PDF ƒx\B(x)? (d) Let Y = X - 10. What is the conditional probability of Y given B = {X ≥ 10}? You can get this by simply transforming ƒx|ß(x) as fy|B(y) = fx|b(y +10). (e) Assume your TV has already lasted 10 years. What is the probability that it fails during the next year?

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