If $X_1$ and $X_2$ are random variables, why is the following inequality true:
$$|\mathbb{E}X_1 - \mathbb{E}X_2| \leq \mathbb{E}|X_1 - X_2|$$
If $X_1$ and $X_2$ are random variables, why is the following inequality true:
$$|\mathbb{E}X_1 - \mathbb{E}X_2| \leq \mathbb{E}|X_1 - X_2|$$
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