I really do need help please 7. X, Y have joint density f(x,y) = 2 if...
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
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)
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).
2. (10 pts The random variables X and Y have joint density function f(x, y) == 22 + y2 <1. Compute the joint density function of R= x2 + y2 and = tan-1(Y/X).
5. (10 pts )The random variables X and Y have joint density function 1 f(x,y) x2 + y2 <1. 3 7T Compute the joint density function of R= x2 + y2 and = tan-'(Y/X).
Is a joint density function? If yes, assume it is the joint density function of r.v.s X and Y , and compute the marginal densities of X and Y . f(r,y) = { " 0 <y<<11 , otherwise
3. (16 points) Suppose that X and Y have the following joint p.d.f. f(x,y) = for 0 < x < y,0 < y <, y 0 otherwise. Compute E[X2]y], the expectation of the conditional distribution of x2 given Y = y.
solve for c such that f(x,y) is a valid density function. Seiten f(x, y) = 1<x<y <3 otherwise 0,
(6 pts) Consider the joint density function f(x, y) = { (9- 2- y), 0<r<3, 3 Sy <6, 0, otherwise Find P(0 < < <1,4 <y<6).
3. Suppose X and Y have joint density f(x,y)- "cy. 0 < x < y < oo, and equal to 0 for all other (r, y). (a) Calculate the joint density of U = Y-X,V-X. (b) Are U and V independent?