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- Use the moment generating function technique to solve. Let X1, . . . , Xn be independent random variables, such that Xi ∼ Exponential(θ), for i =1, . . . , n. Find the distribution of Y = X1 + · · · + Xn.Let a random variable X has the CDF as;Fx(x) = 1 ; x ≥ 1 1/2+x ; 0 ≤ x < 1 0 ; x < 0 Verify that Fx(x) is a CDF. Also- (i) find the PDF of X (ii) Calculate E[ex ] (iii) Determine the probability P[X = 0|X ≤ 0.5]Let Y be a continuous random variable. Let c be a constant. PROVE Var (Y) = E (Y2) - E (Y)2
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