You have an urn containing 20 white balls numbered 1 to 20. First a ball is drawn, and we call the number on the ball drawn X, the ball is replaced in the urn. Then X of the balls are painted red, and they too are put back in the urn. Then 5 balls are drawn, with replacement. LetYbe the number of red balls drawn.

1) Write down the conditional distribution ofYgiven{X=x}, including parameter(s).

2)FindE(Y|X)

3)FindE(Y)

4) Find Cov(X,Y).