Justify each of your answers, this means prove or give a counterexample for each of the questions. a) Let X be a continu

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Justify each of your answers, this means prove or give
a counterexample for each of the questions.
a) Let X be a continuos random variable with distribution Fr. Does there exist a random
1
such that its distribution Fy satisfies Fr(r) = 2Fx(2)?
b) Let X and Y be two independent random variables. Then, for any n, m. € N, is it true
that. E(X"y™) = E(X")E(Y'™)?
c) Let X and Y be two jointly continuous random variables with joint distribution Fx,r and
marginal distributions Ex and Fy, respectively. Suppose there are two numbers a, b € R
such that Fxy(a,b) = Px(a) Fy(b). Does this imply that X and Y are independent?

Justify Each Of Your Answers This Means Prove Or Give A Counterexample For Each Of The Questions A Let X Be A Continu 1 (22.58 KiB) Viewed 14 times

a (10 points) A few unrelated questions. Justify each of your answers, this means prove or give a counterexample for each of the questions a) Let X be a continuous random variable with distribution Fx. Does there exist a random y such that its distribution Fy satisfies Fy(r) = 2Fx()? b) Let X and Y be two independent random variables. Then, for any nm E N, is it true that E(XY) = E(X)E(Ym)? c) Let X and Y be two jointly continuous random variables with joint distribution Fx.y and marginal distributions Fx and Fy, respectively. Suppose there are two numbers a,b ER such that Fx.v(a, b) = Fx(a) Fy(b). Does this imply that X and Y are independent?