I am having trouble when it comes to a pair of random variables. Can you illustrate the procedure of how you think while solving problems like this? Thanks a lot!
2026-03-28 09:54:26.1774691666
Covariance between two random variables
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I will do the expectation part.
$$\mathbb{E}(U) = \mathbb{E}\left(Y - \alpha - \beta X\right)=\mathbb{E}(Y)-\alpha-\beta\mathbb{E}(X) \text{ ......why?}$$
Since
$$\alpha = \mu_Y - \beta \mu_X$$
We have
$$\mathbb{E}(U) = \mathbb{E}(Y) - \mu_Y + \beta\mu_X - \beta\mathbb{E}(X) \text{ ......why?}$$