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For independent X and Y, we have probability density function for them where pdf of X...

For independent X and Y, we have probability density function for them where pdf of X is f(x) = ne^-nx and pdf of Y is f(y) = me^-my. (x and y greater than 0). Let M1=max(X,Y) and M2=min(X,Y). Find cov(M2,M1).

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Answer #1

Independent X and Y, we have probability density function for them where pdf of X is f(x) = ne^-nx and pdf of Y is f(y) = me^-my. (x and y greater than 0).

Cov(M2,M1) = E(M2,M1) = E(M1)E(M2)

Now M2 M1 = max(X,Y) min(X,Y)

= XY always.

E(M2,M1) = E(XY) = E(X) E(Y)

Again M1 + M2 = X + Y always

M1 = (X + Y - M2)

Now

.

Also,

Similarly,

.

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