Back to 16.3 Problems on Conditional Independence, Given a Random Vector

16.3 Exercise 5

Avg difficulty 2.5

Suppose $\left\{N , H\right\}$ is independent and $\left\{N , Y\right\} ci \left|\right. H$ . Use properties of conditional expectation and conditional independence to show that

E \left[\right. g \left(N\right) h \left(Y\right) \left|\right. H \left]\right. = E \left[g \left(N\right)\right] E \left[\right. h \left(Y\right) \left|\right. H \left]\right. a . s .

Pfeiffer, Applied Probability, 16.3 Problems on Conditional Independence, Given a Random Vector, exercise 5

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