Let x be a random variable sampled from distribution $p(x)$. Let $y$ be a random variable sampled from conditional distribution $p(y|x)$.I'd like to express$ \int_{x} \int_{y} f(x, y) p(x)p(y|x)dxdy$ using $\mathbb{E}$ notation.In this case, is it OK to write this by $\mathbb{E}_{x \sim p(x), y \sim p(y|x)} [f(x, y)]$
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