Suppose that X, Y, and Z are three independent random variables. If X, Y N(0, 1)

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Suppose that X, Y, and Z are three independent random variables. If X, Y ∼ N(0, 1) and Z ∼ Exponential(1), find

1. E[XY |Z = 1],

2. E[X2Y2Z2|Z = 1].

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