Suppose that X and Y have joint pmf px yx,y) fxy-/39 for x 1,2 and y...
1. Suppose you have two random variables, X and Y with joint distribution given by the following tables So, for example, the probability that Y o,x - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),J(Y). (b) Find the conditional distribution (pmf) of Y give X, denoted f(YX). (c) Find the expected values of X and Y, EX), E(Y). (d) Find the variances of X and Y, Var(X),Var(Y). (e)...
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
Let the joint pmf of X and Y be defined by x+y 32 x 1,2, y,2,3,4 (a) Find fx(x), the marginal pmf of X. b) Find fyv), the marginal pmf of Y (c) Find P(XsY. (d) Find P(Y 2x). (e) Find P(X+ Y 3) (f) Find PX s3-Y) (g) Are Xand Y independent or dependent?Why or why not? (h) Find the means and the variances of X and Y
Px(x) = The marginal pmf of each of X, Y variables is given below: 1 ; x = -1,3 4 y + 1 2 PY) = ; y = 1,2 - ; x = 1 5 4 0; Otherwise 0; Otherwise (a) If X, Y are independent random variables, then obtain and report the complete joint pmf of X, Y. Provide your answer in a tabular or functional form. (b) Compute the probability that sum of X and Y is...
2. 6. (20points). Let X and Y have the joint pmf ? 1,2,3 , zero elsewhere. (a) Find the mgf M(ti, 2) of this joint distribution. (b) Compute the means and the variances, and the correlation coefficient of X and Y (c) Determine the conditional mean E(Xly)-(extra point)
Q.4 (22') Suppose the joint probability density function of X and Y is fx,y(x, y) = { „) - k(2 - x + y)x 0 sxs 1,0 sys1 o otherwise (a) (7”) Show that the value of constant k = 12 (b) (7') Find the marginal density function of X, i.e., fx(x). (c) (8') Find the conditional probability density of X given Y=y, i.e., fxy(xly). 11
Let X and Y have the joint pmf defined by (х, у) (1,2) (0,0) (0,1) (0,2) (1,1) (2,2) 2/12 1/12 3/12 1/12 1/12 4/12 Pxy (x, y) Find py (x) and p, (y) а. b. Are X and Y independent? Support your answer. Find x,y,, and o, С. d. Find Px.Y
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].
Solve by hand please Is 7a right? Suppose p(x,y)=x+2yxtar=1,2,3, and y=1,2 is the joint pmf of X and Y. 30 Part a: Create the contingency table for X and Y and fill in the marginal probabilities for each variable. Part b: Find the E[X], E[Y], and E[XY). Part c: Find the covariance of X and Y. Part d: Determine if X and Y are independent. My) =429 -+24 1,2,3 __421,2 f(x ) Mc Rica 08 Matlab)
Suppose three random variables X, Y, Z have a joint distribution PX,Y,Z(x,y,z)=PX(x)PZ∣X(z∣x)PY∣Z(y∣z). Then X and Y are independent given Z? True or False Suppose random variables X and Y are independent given Z , then the joint distribution must be of the form PX,Y,Z(x,y,z)=h(x,z)g(y,z), where h,g are some functions? True or false