Let X, Y be random variables with f(x, y) = 1,-y < x < y, 0...

Question

Question

Let X, Y be random variables with f(x, y) = 1,-y < x < y, 0 < y < 1. Show that Cov(X,Y) = 0. Are X, Y independent?

math Statistics-And-Probability

Answer 1

Answer #1

Given that, X and Y are random variables with fi, - y<x<y, 0<y <1 Jxx (x,y)10, elsewhere Marginal of X: Jx (*)= (x2(x,y) dy y

E(X)= ſ tz(x) dx = (1-(0) E(P)= 1 11 (9) dy =12 -(0) Cov(X,Y)=E(XY)- E(X). E(Y) 11.1 231 Now, consider, x(x): 3 y)=1x2y = 2y

Answer 2

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