(Solved): (Accuracy) Let Xi for i=1,,n be independent random variables with E(Xi)= and V(Xi)= ...
(Accuracy) Let Xi? for i=1,?,n be independent random variables with E(Xi?)=? and V(Xi?)=?2 for all i. Let U=nX1?+X2?+?+Xn?? Find the following: (a) E(U) (b) V(U) (c) V(n?U)
(a) We know that the expected value of a sum of random variables is the sum of their expected values. Using this property, we have:
E(U) = E(X1 + X2 + ... + Xn) = E(X1) + E(X2) + ... + E(Xn) =
E(U) =