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368概率中等数值题short

Second Moment of a Scale-Mixed Normal via Tower

题目

Let Θ\Theta be drawn uniformly from {1,2,3}\{1, 2, 3\} and, given Θ=θ\Theta = \theta, let XΘ=θN(0,θ)X \mid \Theta{=}\theta \sim N(0, \theta). Using the tower property, compute E[X2]E[X^2] and E[X4]E[X^4].

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你的答案

E[X^2]

E[X^4]