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
(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).
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.
(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).
1. The joint pmf of X and Y is given by the table 20.1 0.1 0.1 0.1 50.2 0 00 60.1 0.1 0.1 0.1 (a) Determine the (marginal) pmf of X and of Y (b) Are X and Y independent? (c) Calculate Cov(X, Y).
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.
you have two random variables, X and Y with joint distribution given by the following table: Y=0 | .4 .2 4+.26. So, for example, the probability that Y 0, X - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),f(r). (b) Find the conditional distribution (pmf) of Y give X, denoted f(Y|X). (c) Find the expected values of X and Y, E(X), E(Y). (d) Find the variances of X...
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.
Suppose that X and Y have joint pmf px yx,y) fxy-/39 for x 1,2 and y 2,3 0elsewhere). a) Determine the marginal pmfs px(x) and py(y) b) Determine the conditional pmf of px(xly). c) Are X and Y independent? Give a clear determination using probability formulas.