3. Let (X, Y) be a bivariate random variable with joint pmf given by x= 1,2,3, y = 0,1,2,3, ... ,00 f(x, y) 12 0 e.w. (a) Show that f(x, y) is a valid joint pmf. (b) Find fa(x) (i.e. the marginal pmf of X). (c) Find fy(y) (i.e. the marginal pmf of Y). (d) Find P [Y X]
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
4. Assume that the joint pmf of (X,Y) is 0.20 0.10 0.05 0.25 0.10 Find (1) a: (2) P(XYs1): (3) the marginal distributions. Mark
1. Consider a discrete bivariate random variable (X,Y) with the joint pmf given by the table: Y X 1 2 4 1 0 0.1 0.05 2 0.2 0.05 0 4 0.1 0 0.05 8 0.3 0.15 0 Table 0.1: p(, y) a) Find marginal distributions of X and Y, p(x) and pay respectively. b) Find the covariance and the correlation between X and Y.
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(X-0,Y<1). Find the marginal PMFs of X and Y. Find P(Y-1X-0). Are X and Y independent?
(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)
Let the joint pmf of X and Y be p(x, у) схуг, x-1,2,3, y-12. a) Find constant c that makes p(x, y) a valid joint pmf. c) Are X and Y independent? Justify d) Find P(X+Y> 3) and PCIX-YI # 1)
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].
Problem 4 Let X and y be independent Poisson(A) and Poisson(A2) random variables, respectively. i. Write an expression for the PMF of Z -X + Y. i.e.. pz[n] for all possible n. ii. Write an expression for the conditional PMF of X given that Z-n, i.e.. pxjz[kn for all possible k. Which random variable has the same PMF, i.e., is this PMF that of a Bernoulli, binomial, Poisson, geometric, or uniform random variable (which assumes all possible values with equal...
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