Let $X \in \mathbb{R}^{m}$ and $W \in \mathbb{R}^{p}$ random vectors. Does $E[X|W] = 0 \implies E[XW^{T}]=0$?
2026-04-22 09:37:20.1776850640
$E[X|W] = 0 \implies E[XW^{T}]=0$?
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Hint
$$\mathbb E[XW^T]=\mathbb E\big[\mathbb E[XW^T\mid W]\big].$$