1 suppose that the random variables x and y are independent, Ask an Expert

Statistics

1. Suppose that the random variables X and Y are independent and N (0, σ2)- distributed.

(a) Show that X/Y ∈ C(0, 1).

(b) Show that X + Y and X - Y are independent.

2. Suppose that the moment generating function of (X, Y )t is ψX,Y (t, u) = exp{2t + 3u + t2 + atu + 2u2}. Determine a so that X + 2Y and 2X - Y become independent.

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