Let $E(x)$ be the expected value of random variable $x$. $c$ is a constant, then what will be the $E(cx)$ in simplest form and why?
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$\begingroup$For the discrete case: $$ \mathbf{E} \varphi(X)=\sum_{k=0}^{\infty}c k p_k= c \sum_{k=0}^{\infty}k p_k = c \mathbf{E}X $$
that's if I understand your question correctly, of course.
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