Mathematics, 26.09.2019 21:10, DroctorWellsfan

If x1, x2 , , xn are independent rvs, each with the same mean value m and variance s2 , then we have seen that e(x1 + x2 + + xn) ¼ nm and v(x1 + x2 + + xn) ¼ ns2 . in some applications, the number of xi’s under consideration is not a fixed number n but instead a rv n. for example, let n be the number of components of a certain type brought into a repair shop on a particular day and let xi represent the repair time for the ith component. then the total repair time is sn ¼ x1 + x2 + + xn, the sum of a random number of rvs. a. suppose that n is independent of the xi’s. obtain an expression for e(sn) in terms of m and e(n). hint: [refer back to the theorem involving the conditional mean and variance in section 5.3, and let y ¼ sn

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If x1, x2 , , xn are independent rvs, each with the same mean value m and variance s2 , then we hav...