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You have 6 tiny cheapo generators powering your house. If at least 4 out of the 6 generators are working then your air conditioner works. Each generator functions independently of other generators. The pdf of the amount of time a generator works before it permanently breaks is given by f(x) = K for x > 1, and 0 otherwise %3D x4 for some constant K. Assume that you start all the generators at the same time and let X be the amount of time your air-conditioner works. Find (i) the pdf of X (ii) E[X] (iii) Var(X). Do not have any unknown constants in your answers.

You have 6 tiny cheapo generators powering your house. If at least 4 out of the 6 generators are working then your air conditioner works. Each generator functions independently of other generators. The pdf of the amount of time a generator works before it permanently breaks is given by f(x) = K for x > 1, and 0 otherwise %3D x4 for some constant K. Assume that you start all the generators at the same time and let X be the amount of time your air-conditioner works. Find (i) the pdf of X (ii) E[X] (iii) Var(X). Do not have any unknown constants in your answers.

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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You have 6 tiny cheapo generators powering your house. If at least 4 out of the 6 generators are working then your air conditioner works. Each generator functions independently of other generators. The pdf of the amount of time a generator works before it permanently breaks is given by f(x) : K for x > 1, and 0 otherwise for some constant K. Assume that you start all the generators at the same time and let X be the amount of time your air-conditioner works. Find (i) the pdf of X (ii) E[X] (iii) Var(X). Do not have any unknown constants in your answers.
Transcribed Image Text:You have 6 tiny cheapo generators powering your house. If at least 4 out of the 6 generators are working then your air conditioner works. Each generator functions independently of other generators. The pdf of the amount of time a generator works before it permanently breaks is given by f(x) : K for x > 1, and 0 otherwise for some constant K. Assume that you start all the generators at the same time and let X be the amount of time your air-conditioner works. Find (i) the pdf of X (ii) E[X] (iii) Var(X). Do not have any unknown constants in your answers.
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