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Suppose X,Y are discrete random variables, each taking only twodistinct values.Prove that if E(XY)=E(X)E(Y) then X,Y are independent (Be awarethat you have to prove E(XY) =E(X)E(Y) -> X,Y independent andNOT the converse)
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SOLVED: Let X and Y be independent random variables with exponential distribution, with parameters λx and λy respectively:(a) Find fX(x) and fY(y).(b) What is the joint probability density function (PDF) fX,Y(x,y)?(c) Define Z = X Y. Express P(Z < 2) in terms of a double integral over x and y.(d) Compute FZ(z).(e) Compute fZ(z).
SOLVED: Let X and Y be independent random variables wit…
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