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 
Consider the following joint pmf of random variables X and Y. Y = 0 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].
6. (20%) Consider two random variables X and Y with the joint PMF given in Table 2. Table 2: Joint PMF of X and Y Y =0Y 1 X 0 X 1 0 (a) (5%) Find the PMF of X and PMF of Y. (b) (5%) Find EX, EY, Var(X), Var(Y (c) (10%)Find the MMSE estimator of X given Y, (M) for both Y 0 and Y 1
6 X and Y are two discrete random variables with the following PMF. IN IN IA. a.  Find the marginal pmf's for X and Y. b. Draw the joint CD c. Calculate the probability of the events: A(X>0), B (xeY), and CX Y for the 3 pt 3 pt. indicated PMF t. Are X, Y independent? Prove. 2 pt. t.
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
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(YX). (c) Find the expected values of X and Y, E(X), E(Y). (d) Find the variances of X...
ciule jolh! PMF and the marginal PMFs? 6.14 Let X and Y be discrete random variables. Show that the function p: R2 R defined by p(r, y) px(x)pr(y) is a joint PMF by verifying that it satisfies properties (a)(c) of Proposition 6.1 on page 262. Hint: A subset of a countable set is countable CHAPTER SIX Joindy Discrete Random Variables 6.2 Joint and marginal PMFs of the discrete random variables x numher of bedrooms and momber of bwthrooms of a...
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)...
Table 1 Joint PMF of X and Y in Example 5.1 x=01 X=1  1 Fig. 1 shows PXY()PXY( JointPMF ? 2 Fig. 1. Joint PMF of X and Y (Example 5.1). a. b. c. d. Find P(X0,Y<1). Find the marginal PMFs of X and Y. Find P(Y1X0). Are X and Y independent?
Consider the following joint probability density function of the random variables X and Y : 3x−y , 1 < x < 3, 1 < y < 2, f(x, y) = 9 0, elsewhere. (a) Find the marginal density functions of X and Y . (b) Are X and Y independent? (c) Find P(X > 2).
(1) Suppose the following is the joint PMF of random variables X and Y P(X x,Y y) c(3x + y), x1,2, y 1,2 where c is an unknown constant a. What is the value of c that makes this a valid joint PMF? b. Find Cov(X, Y)