Independent random variables


Suppose X1 and X2 are independent random variables, each uniformly distributed over the set {±1}; that is, each Xi takes the value -1 with probability 1/2 and the value 1 with probability 1/2. (a) Compute E[X1 + X2]. (b) Compute E[(X1 + X2)2]. (c) Generalize part (b) to n random variables: compute E[(X1 + ... + Xn )2 ], where each of the Xi's are uniformly distributed over {±1} here, you may assume that the Xi's are pairwise relatively prime, which means that for every pair of distinct indices i and j, the variables Xi and Xj are independent.

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Basic Statistics: Independent random variables
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