Let Y and Z be two random variables, how to show that $$ Y^2 \ge [E(Y|Z)]^2$$
Can anyone give me any hint or idea of how to do this? Thanks in advance.
2026-03-26 08:04:23.1774512263
How to show that $Y^2 \ge [E(Y|Z)]^2$
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This result is false. Consider the case when $Y$ and $Z$ are independent; then $\mathbb E[Y \mid Z] = \mathbb E[Y]$.