goldy1490 goldy1490

16-12-2022
Mathematics

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For each of the following statements, explain whether it is true or false. If you think it is true, then prove why you think it is always true. If you believe it is false, then giving a counterexample is sufficient. (a) (7 points) IfXandYare independent, thenE[X/Y]=E[X]/E[Y]. (b)(7points)E[g(X,Y)â£Y=y]=E[g(X,y)]. (c) (7 points) LetXandYare two random variables, thenvar(Y)>var(E[Yâ£X]). (d) (7 points)E[E[Xâ£Z]â£Y]=E[Xâ£Z]. (e) (7 points) LetXandYbe continuous random variables andNbe a discrete random variable. IfX,Y,Nare independent, thenE[E[Xâ£Y,N]â£N]is a number.

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