2. Denote by X and Y the lengths of life, in hundreds of hours, for components of types I and II, respectively, in elect

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2 Denote By X And Y The Lengths Of Life In Hundreds Of Hours For Components Of Types I And Ii Respectively In Elect 1 (161.82 KiB) Viewed 26 times

2. Denote by X and Y the lengths of life, in hundreds of hours, for components of types I and II, respectively, in electronic system. The joint density function of X and Y is given by | xe-(x+y)/2, x>0,y>0, f(x,y) = 0, elsewhere ( (a) Find the marginal distribution of X and Y. (b) Are the two random variables X and Y independent? Justify your answer. (C) What is the probability that the type II component will last more than 200 hours? (d) One way to measure relative efficiency of the two components is to compute the ratio Y R:= X Find the expected value of the relative efficiency R. (17 marks)