Question 12: Let X and Y have the joint probability density function Find P(X>Y), P(X Y...
(1 point) 1. (Old Quiz Question) Let X and Y have the joint probability density function 1 for 01,0 y< 1 0 elsewhere (a) Calculate P(X-Y < 0.5) (b) Calculate PXY 0.25) (c) Find P(X 0.75|XY>0.25)
Suppose a joint probability density function for two variables X and Y is given as follows: {24x0, if 0 < x < 1,0 < y < 1 f(x, y) = otherwise Please find the probability p (w > 1) =? 3
If X and Y have a joint probability density function specified by 2-(+2y) find P(X <Y).
Let X and Y have joint probability density function fx,y(x,y) = e-(z+y) for 0 x and 0 y. Find (a) Pr(X=y (b) Prmin(X, Y) > 1/2) (c) Pr(X Y) d) the marginal probability density function of Y (e) E[XY].
(1 point) 1. (Old Quiz Question) Let X and Y have the joint probability density function for 0 x elsewhere f(x, y)={1 f(x, y) = 1,08 ysl 0 (a) Calculate P(X - Y < 0.5) (b) Calculate P(XY <0.25) (c) Find P(X 0.75 IXY 〉 0.25)
Let the joint pmf of X and Y be p(x, у) схуг, x-1,2,3, y-12. a) Find constant c that makes p(x, y) a valid joint pmf. c) Are X and Y independent? Justify d) Find P(X+Y> 3) and PCIX-YI # 1)
4. Let X and Y have joint probability density function f(x,y) = 139264 oray3 if 0 < x, y < 4 and y> 4-1, otherwise. (a) Set up but do not compute an integral to find E(XY). (b) Let fx() be the marginal probability density function of X. Set up but do not compute an integral to find fx(x) when I <r54. (c) Set up but do not compute an integral to find P(Y > X).
(1 point) Let x and y have joint density function p(2, y) = {(+ 2y) for 0 < x < 1,0<y<1, otherwise. Find the probability that (a) < > 1/4 probability = (b) x < +y probability =
Let X and Y be two continuous random variables having the joint probability density 24xy, for 0 < x < 1,0<p<1.0<x+y<1 0, elsewhere Find the joint probability density of Z X + Y and W-2Y.
Find the probability that Y is greater than 3. Let Y have the probability density function f(y) = 2/y3 if y> 1, f(y) = 0 elsewhere.