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Let X_{1},..., X_{n} be iid random variables with expected value 0, variance 1, and covariance Cov[X_{i}, X_{j}] = ρ. Use Theorem 5.13 to find the expected value and variance of the sum Y = X_{1} +···+ X_{n}.
Theorem 5.13
X is an n-dimensional random vector with expected value µ X, correlation R_{X}, and covariance C_{X}. The m-dimensional random vector Y = AX + b, where A is an m × n matrix and b is an m-dimensional vector, has expected value µY, correlation matrix R_{Y}, and covariance matrix C_{Y} given by
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