2. The joint pmf of X and Y is given below. f(x,y) 0 1 2 Y 0 1/10 3/100 1 3/10 2/10 1/10 a. Compute P(Y = 0|1 < X < 2). b. Compute E(X|Y = y) for y = 0,1. C. Evaluate Ey[E(X|Y)] using the formula Ey [E(X|Y)] = {y E(X|Y = y) f (y) and the results of part (b). d. Evaluate E(X) using the formula E(X) = Exxfx(x). Note that your answers in (c) and (d) should...
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
The joint pmf of X and Y is defined by f(x,y)=, x=1,2; y=1,2 (a) Find Cov(X,Y). (b)Find E(X|Y=1) x + 2y 18
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
The following table presents the joint probability mass function pmf of variables X and Y 0 2 0.14 0.06 0.21 2 0.09 0.35 0.15 (a) Compute the probability that P(X +Y 3 2) (b) Compute the expected value of the function (X, Y)3 (c) Compute the marginal probability distributions of X and )Y (d) Compute the variances of X and Y (e) Compute the covariance and correlation of X and Y. (f) Are X and Y statistically independent? Clearly prove...
. For > 0 and A > 0, define the joint pdf -Ay = 0<x<A,<y, fx.y(,y) 10 else. (a) Express c in terms of X and A. (b) Find E[XY]. (c) Let [2] be the largest integer less than or equal to z. For example, (3.2] = 3 and [2] = 2. Find the probability that [Y] is even, given that 4 <x< 34
3. Let f(x,y) = xy-1 be the joint pmf/ pdf of two random variables X (discrete) and Y (continuous), for x = 1, 2, 3, 4 and 0 <y < 2. (a) Determine the marginal pmf of X. (b) Determine the marginal pdf of Y. (c) Compute P(X<2 and Y < 1). (d) Explain why X and Y are dependent without computing Cou(X,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?
Can you just solve 3-6 please? Qi Suppose X and Y have the following joint PMF. x\y 2 4 8 -1 0 0 1/10 1/5 2/5 0 0 0 1/10 1 1/5 1. Find the marginal P.M.F. for Y, then find E(Y) and Var(Y). 2. Find E(X), the expected value for the absolute value of X. 3. Find the conditional P.M.F. for Y given that \X] = 1, then find E(Y||X| = 1) and Var(Y||X| = 1). 4. Find Cov(X,Y)....