problem: (X,Y) has joint pdf f(x,y) = 2 for 1 x < y 2 and f(x,y) =0 otherwise. Y

Q: problem: (X,Y) has joint pdf f(x,y) = 2 for 1 x < y 2 and f(x,y) =0 otherwise. Y

(xy) (1/(2-x)) dy) dx E(Y/X=x) = -3

ID: 3133910 • Letter: P

Question

problem: (X,Y) has joint pdf f(x,y) = 2 for 1 x < y 2 and f(x,y) =0 otherwise. You found the marginal pdfstobefX(x)=2(2-x)for1x2andfX(x)=0otherwiseandfY(y)=2(y-1)for1y2andfY(y)=0 otherwise.

(a) For what x’s is the conditional pdf fY|x(y) defined?

(b) Give the conditional pdf of Y given that X=x, i.e., fY|x(y).

(c) Find the mean of the conditional distribution of Y given that X=x, i.e., Y|x = E(Y|X=x). You may use that the mean of a uniform distribution on (a,b) is (a+b)/2.

(d) is E(Y|X=x) a linear function of x?