(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).
(pts) 1. The joint probability density of X and Y is given by . 0<x<1 and 0 <y<2 otherwise d) Find Cov(X,Y). a) Verify that this is a joint probability density function. b) Find P(x >Y). ) Find Pſy>*<51 c) Find the correlation coefficient of X and Y (Pxy).
E = "Expected Value" V = "Variance" 0 < x < 00, x < y < oo IS joint probability density function a) Compute the probability that X < 1 and Y < 2. b) Find E(X) c) Find E(Y d) Find V(X) e) Find V(Y)
the answer should be 1/2 +x 4. Let X and Y joint density function ( 2e-2(x+y) if 0<r<y< f(x,y) = elsewhere. What is the expected value of Y, given X = x, for x > 0?
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.
4.5-5 Two random variables X and Y have a joint probability density function ability, 0<y<x<2 om oldalon ( 52 fxy(x, y) = 16 o Wes and m Signal es elsewhere to (a) Find the marginal density functions of X and Y. (b) Are X and Y statistically independent? oldoro ototitillarindanand
(1 point) The joint probability density function of X and Y is given by f(x, y) = cx – 16 c”, - <x< 0 < b < co alt 0 < y < 0 Find c and the expected value of X: c = E(X) =
If X and Y have a joint probability density function specified by 2-(+2y) find P(X <Y).
5. Given the probability density f(x)= for -0<x<00, find k. 1+ 2 Jor -
The joint density function of X and Y is J x +y if 0 < x,y<1 f(x, y) = 3. otherwise. a) Are X and Y independent? b) Find the density of X. c) Find P(X + Y < 1).