1) Let random variables X and Y have the joint PMF: otherwise a) Calculate the value of c b) Specify the marginal PMFs Pr(x) and P- c) Calculate P[X +Y<0].
We have the following joint PMF of X and Y: Pxy (x,y) ſa(x+3y) x =1,2,3; y =1,2 0 otherwise Find: 1. the value of a 2. the marginal PMFs of X and Y 3. if X and Y are independent
271 Exercise 1/1.4. Consider the joint pmf p(x, y) = cxy. 1 sxsy <3. (a) Find the normalizing constant c. (b) Are X and Y independent? Prove your claim. (c) Find the expectations of X, Y, XY.
(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).
(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).
Consider the following joint pmf of random variables X and Y. Y = 0 Y = 1 X = 0 1/6 1/4 X = 1 1/4 1/3 Find the marginal pmfs of X and Y. Are the random variables X and Y independent?
3. (a) Let (X,Y) have the joint pmf (2 + y + k – 1)! P(X = 1, Y = y) => pip (1- P1 - p2), r!y!(k − 1)! where r, y=0,1,2, ..., k> 1 is an integer, 0 <P1 <1,0 <p2 <1, and p1 + P2 <1, find the marginal pmfs of X and Y and the conditional pmf of Y given X = r.
1) Let X and Y have joint pdf: fxy(x,y) = kx(1 – x)y for 0 < x < 1,0 < y< 1 a) Find k. b) Find the joint cdf of X and Y. c) Find the marginal pdf of X and Y. d) Find P(Y < VX) and P(X<Y). e) Find the correlation E(XY) and the covariance COV(X,Y) of X and Y. f) Determine whether X and Y are independent, orthogonal or uncorrelated.
Find the normalization constant c and the marginal pdf's for the following joint pdf fxy(x, y) = ce-*e-y for 0 Sysx < 0
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)