If X is a random variable and $E(X)$ is expectation of $X$. Another random variable, $Y$, is defined in terms of $X$ such that $Y = X - E(X)$. Prove that $E(Y) = 0$.
2026-02-22 22:50:30.1771800630
prove that $E(Y) = 0$ if $X$ is a random variable and $Y = x- E(x)$
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$\mathbb{E}Y = \mathbb{E}(X - \mathbb{E}X) = \mathbb{E}X - \mathbb{E}(\mathbb{E}X) = \mathbb{E}X - \mathbb{E}X = 0$