Let X1 and X2 be two normal random variables. Suppose X1 is distributed as N(µ1,o3), and X2 is distributed as N(µ2,03). Suppose X1 and X2 are independent. 1. Let Y1 = 3X1. Find the distribution of Y1 and prove it. 2. Let Y2 = X1 – X2. Find the distribution of Y2 and prove it. (Hint: One can use the moment generating function of normal distribution.)

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