2. (15%) Let X1 and X2 be two independent random variables and both of then follow a standard normal distribution. Let Y = .Please find the probability density function of Y.

3. (10%) Assume that X is a random variable with a probability density function f(x) that is positive and continuous when a ＜ x ＜ b; zero elsewhere. The distribution function F(x) of X may be written F(x) = 0 when x ≤ a, and F(x) = 1 when x ≥b. Assume that there is a number M of the distribution with F(M)=0.3. Let X1, X2 and X3be a random sample from this distribution. LetY1＜Y2 ＜Y3 denote the order statistics of the sample. Please compute the value of Pr(Y2 ＜ M).

2. (15%) Let X₁ and X₂ be two independent random variables and both of then follow a standard normal distribution. Let Y = .Please find the probability density function of Y.

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