Question
Let $X_1,X_2,$ and $X_3$ be uncorrelated random variables with $\var{X_i} = \sigma_i^2$, $i = 1,2,3$. Define $U = X_1 + X_2$ and $V = X_1 + X_3$. Compute $\corr{U}{V}$ when $\sigma_1^2 = 256, \sigma_2^2 = 144,$ and $\sigma_3^2 = 1344$.
easy Probability
Summy Cov
A release-checked easy problem for training Covariance/Correlation.
Practice focus
This Probability problem is tagged Covariance/Correlation. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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