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Q4. (10 marks) Let X1 and X2 be two independent random variables. Suppose each Xi is exponentially distributed with parameter ii. Let Y=Min (X1, X2). A) (5 marks) Find the pdf of Y. B) (5 marks) Find EO'). Hint: Let Y = Min (X1, X2). 1-P[Y > c] = 1'le (X1, X2) > C] = P[X1> 0, X2 > 0] 2. Obtain the pdf of Y by differentiating its cdf of Y. Q5. (10 marks) Let X1, . . . , X11 be random variables corresponding to n independent bids for an item on sale. Suppose each Xi is uniformly distributed on [100, 200]. If the seller sells to the highest bidder, what is the expected sale price? A) (5 marks) Find the pdfofW = Max (X1, X2, .. ., X\"). B) (5 marks) Find E(W). Hint. Let W = Max (X1, X2, . . ., X11). 1.P[W S c] = P[Max (X1, X2, ...,XD):I c]=P[X1 c, X2 :1 c,..., XnSc] 2. Obtain the pdf of W by differentiating its cdfof W. Q2. (10 marks) Given the random variables X and Y having the following joint density: f(x, y) = 2(x + y) for 0