Question
Let $X_1$ and $X_2$ be a pair of random variables. Show that the covariance between the random variables $Y_1=\left(X_1+X_2\right)$ and $Y_2=\left(X_1-X_2\right)$ is 0 if and only if $X_1$ and $X_2$ have the same variance.
Step 1
The covariance of two random variables $Y_1$ and $Y_2$ is defined as: \[ \operatorname{Cov}(Y_1, Y_2) = E[(Y_1 - E[Y_1])(Y_2 - E[Y_2])] \] where $E[\cdot]$ denotes the expectation. Show more…
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Key Concepts
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