Let x and y be independent geometric distributions u minxy

Assignment Help Basic Statistics

Let X and Y be independent geometric distributions. U = min(X,Y), V = X - Y

(a) Show that U and V are independent

(b) Find the distribution of Z = X / (X+Y)

Suppose the distribution of Y, conditional on X = x, is N(x, x^2), and marginal of X is U[0,1].

(a) Find E[Y], Var[Y], Cov(X, Y)

(b) Are the random variables U = Y / X and V = X independent?

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