### An n-dimensional random vector with expected value

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Let X1,..., Xn be iid random variables with expected value 0, variance 1, and covariance Cov[Xi, Xj] = ρ. Use Theorem 5.13 to find the expected value and variance of the sum Y = X1 +···+ Xn.

Theorem 5.13

X is an n-dimensional random vector with expected value µ X, correlation RX, and covariance CX. 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 RY, and covariance matrix CY given by #### Calculate the expected value and standard deviation

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