Question: 1. Problem 13.4 The random variables X1 and X2 are N(1,2 1) and N(2,2 2) distributed. Let the random variable V be distributed as X1

1. Problem 13.4 The random variables X1 and X2 are N(μ1,σ2 1) and N(μ2,σ2 2)

distributed. Let the random variable V be distributed as X1 with given proba bility p and as X2 with probability 1 − p. What is the probability density of V?Is this probability density the same as the probability density of the random variable W = pX1 +(1− p)X2 when X1 and X2 are independent?

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