If $X_{1}, X_{2}, X_{3},$ and $X_{4}$ are (pairwise) uncorrelated random variables, each having mean 0 and variance $1,$ compute the correlations of (a) $X_{1}+X_{2}$ and $X_{2}+X_{3}$ (b) $X_{1}+X_{2}$ and $X_{3}+X_{4}$
Added by David W.
Step 1
Recall that the covariance of two random variables $A$ and $B$ is given by $\text{Cov}(A, B) = E[AB] - E[A]E[B]$. Since the mean of each random variable is 0, this simplifies to $\text{Cov}(A, B) = E[AB]$. (a) We want to find the correlation between $X_1 + X_2$ Show more…
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