Let X and Y be independent uniform random variables on (0,1). a) Find the variance of Z1=min(X,Y). b) Find the variance of Z2 = max(X,Y).
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Let X and Y be independent uniform random variables on (0,1).
a) Find the variance of Z1=min(X,Y).
b) Find the variance of Z2 = max(X,Y).
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- Suppose that the lifetime, X, and brightness, Y, of a light bulb are modeled as continuous random variables. Let their joint pdf be given by:f(x,y)=λ_1λ_2e^{-λ_1x-λ_2y},x,y>0 •Are lifetime and brightness independent?•Are lifetime and brightness uncorrelated?Let X1 and X2 be independent chi-square random variables with r1 and r2 degrees of freedom, respectively. Let Y1=(X1/r1)/(X2/r2) and Y2=X2. (a) Find the joint pdf of Y1 and Y2.Let random variables X and Y have the joint pdf fX,Y (x, y) = 4xy, 0 < x < 1, 0 < y < 1 0, otherwise Find the joint pdf of U = X^2 and V = XY.
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