Let f(x, y) = kxy, for 0 <x< 1 and 0 <y<1 and 0 elsewhere, a) Find k b) Find marginal pdfs. c) Are X and Y independent? d) Find P(X<0.5, Y>0.5).
5. Let ffx)= cx for 1 < x< c0, zero otherwise be the pdf for the random variable X. a) Find c b) Find F(x). c) Find P(X> 3.2). d) Find E(X).
provided that tihe expettauIO 1.8.10. Let f(z) = 2r, 0 < z < i, zero elsewhere, be the pdf of X. (a) Compute E(1/X). (b) Find the edf and the pdf of Y 1/X c) Compute E(Y) and compare this result with the answer obtained in Part (a).
For f(x, y) = k(x2 + y2), 0<x< 1 and 0 <y<1 and 0 elsewhere: a) Find k. b) Are X and Y independent? c) Find P(X<0.5, Y>0.5), P( X = 0.5, Y>0.5).
2) Suppose that X has density function f(a)- 0, elsewhere Find P(X < .3|X .7).
Let (X,Y) have joint pdf given by f(x, y) = { Sey, 0 < x <y<, | 0, 0.W., (a) Find the correlation coefficient px,y (b) Are X and Y independent? Explain why.
(b) Let X have the pdf x? f(x)= ;-3<x<3, 18 = zero elsewhere. (i) Find the cdf of X
2. Let Px(x) = 1, X = 1,2,3, 4, 5, zero elsewhere, be the pmf of X. Find P(X = 1 or 2), P(3 < X < ), and P(1 < X < 2).
Let (X,Y) have joint pdf given by sey, 0 < x < y < 0, f(x, y) = { ( 0, 0.W., (a) Find the correlation coefficient px,y: (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
Suppose that f (x II 2y), 0 < x < 1,0 < y < 1. Find EX + Y).