2. An industrial rm is concerned about the longevity of light-bulbs produced in one of their factories. For 'i = l, . . . , a let X,- be a collection of independent and identi- cally distributed random variables, each of which denotes the lifetime (in days) of a corresponding light-bulb in a size-n simple random sample, with probability densit}r function 1 I exp , :L' > 0 mar) = A { A} U, :L' g 0 where A > 0. Let Y = min(X 1-. . . . ,Xn), and determine the cumulative density func- tion, probability density function, expectation, and variance of Y. X1 3. Let X1 and X2 be as in the previous problem. Compute the expected value of X1+X2