3. (16 points) Suppose that X and Y have the following joint p.d.f. f(x,y) = for...
(50 points) Suppose that the joint p.d.f. of X and Y is as follows: for x 2 0, y 2 0, and x + y <1 elsewhere 2. 24xy f(x)0 a) Determine the value of P(X < Y). b) Determine the marginal p.d.f.'s for Xand Y c) Find P(X> 0.5) d) Determine the conditional p.d.f. of X|Y = 0.5 e) Find P(X> 0.5|Y 0.5) f) Find P(X> 0.5|Y> 0.5) g) Find Cov (X, Y)
QUESTION 12 Let the random variable X and Y have the joint p.d.f. f(x,y) =(zy for 0< <2, 0 < y <2, and z<y otherwise Find P(0KY <1) 16 QUESTION 13 R eter to question 12. Find P(o < x <3I Y-1).
I really do need help please 7. X, Y have joint density f(x,y) = 2 if 0 < r <y< 1, S(x, y) = 0 otherwise. Compute the conditional density fxiy
2. Suppose X and Y are continuous random variables with joint density function f(x, y) = 1x2 ye-xy for 1 < x < 2 and 0 < y < oo otherwise a. Calculate the (marginal) densities of X and Y. b. Calculate E[X] and E[Y]. c. Calculate Cov(X,Y).
7. Suppose that the joint density of X and Y is given by f(x,y) = e-ney, if 0 < x < f(z, y) = otherwise. Find P(X > 1|Y = y)
7.695 points Save Answer QUESTION 4 Let the random variable X and Y have the joint p.d.f. for 0 < x < 1, 0 < y < 1, and 0 < x +y < 1 | 24cy f(x, y) = { lo otherwise Find E[X].
2. Let X and Y have joint density f(x.v) = \ şcy? if 0 <x< 1 and 1 <y<2, otherwise. (a) Compute the marginal probability density function of Y. If it's equal to 0 outside of some range, be sure to make this clear. (b) Set up but do not compute an integral to find P(Y < 2X).
4. Suppose X and Y have the joint pdf f(x,y) = 6x, 0 < x < y < 1, and zero otherwise. (a) Find fx(x). (b) Find fy(y). (c) Find Corr(X,Y). (d) Find fy x(y|x). (e) Find E(Y|X). (f) Find Var(Y). (g) Find Var(E(Y|X)). (h) Find E (Var(Y|X)]. (i) Find the pdf of Y - X.
this is the answer 7. Let X and Y have joint density (x + y) for 0 < 2y 52 51 f(x, y) = ? otherwise. What is the conditional expectation of X given Y =y? We were unable to transcribe this image
8), Let X and Y be continuous random variables with joint density function f(x,y)-4xy for 0 < x < y < 1 Otherwise What is the joint density of U and V Y