If X and Y have a joint probability density function specified by 2-(+2y) find P(X <Y).
(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 =
1. (10) Suppose the random variables X and Y have the joint probability density function 4x 2y f(x, y) for 0 x<3 and 0 < y < x +1 75 a) Determine the marginal probability density function of X. (6 pts) b) Determine the conditional probability of Y given X = 1. (4 pts)
< 1. The joint probability density function (pdf) of X and Y is given by for(x, y) = 4 (1 - x)e”, 0 < x <1, 0 < (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY).
Question 12: Let X and Y have the joint probability density function Find P(X>Y), P(X Y <1), and P(X < 0.5)
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
Q1. Let X and Y have joint density 0, otherwise. a. Find the marginal densities of X and Y b. Find P(0.2 < Y < 0.31X = 0.8).
. Let X and Y be the proportion of two random variables with joint probability density function f(r, y) e-*, 0, if, 0 < y < x < oo, elsewhere. a) Find P(Xc3.y-2). b) Are X and Y independent? Why? c) Find E(Y/X)
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.
Consider fx (x)=e*, 0<x and joint probability density function fx (x, y) = e) for 0<x<y. Determine the following: (a) Conditional probability distribution of Y given X =1. (b) ECY X = 1) = (c) P(Y <2 X = 1) = (d) Conditional probability distribution of X given Y = 4.
(8pts) 1. The joint probability density of X and Y is given by + 0<x<1 and 0 <y< 2 otherwise a) Verify that this is a joint probability density function. b) Find P(x >Y). o) Find Pſy > for< d) Find Cov(X,Y). e) Find the correlation coefficient of X and Y (Pxy).