(a) Give the marginal density functions for both random variables. Are the independent? (b) What is the probability that the lives of X component will exceed 2 hours given that the life of Y did not exceed 5 hours?

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Two electronic components of a missile system work in harmony for the
success of the total system. Let X and Y denote the life in hours of the two
components. The joint density of X and Y is
f(x,y) = y e-y(1+x) ,
х, у > 0
(a) Give the marginal density functions for both random variables. Are the
independent?
(b) What is the probability that the lives of X component will exceed 2 hours
given that the life of Y did not exceed 5 hours?
Transcribed Image Text:Two electronic components of a missile system work in harmony for the success of the total system. Let X and Y denote the life in hours of the two components. The joint density of X and Y is f(x,y) = y e-y(1+x) , х, у > 0 (a) Give the marginal density functions for both random variables. Are the independent? (b) What is the probability that the lives of X component will exceed 2 hours given that the life of Y did not exceed 5 hours?
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