Let x1 xnnbspbe iid random variables with expected value 0

Question

Let X₁,..., 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 = X₁ +···+ 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