The discrete random vector (X, Y) has a joint probability mass function fx.y(x, y) described in t...
20. (8 points) Suppose X, Y, and Z are discrete random variables with joint probability mass function P(x, y, z) given below. Be sure to full justify your answers and show ALL work. P(0,0,0) = 2,3 P(0,0,1) 33 P(0,1,0) = P(1,0,0) = 32 P(1,0,1) = P(1,1,0) = 32 a. Find the marginal probability mass function for 2, pz(2). b. What is E[X | Y = 0]? P(0,1,1) = 4 P(1,1, 1) = 32
7. Let X and Y have joint probability mass function fx.y(x,y) = (x+y)/30 for x = 0.1, 2.3 and y0,1,2. Find (a) PrX 2,Y-1) (b) PrX>2,Y S1) (c) Pr(X + Y=4) (d) Pr[X >Y) (e) the marginal probability mass function of Y, and (f) E[XY]
4. The random variables X and Y have joint probability density function fx.y(r, y) given by: else (a) Find c (b) Find fx (r) and fr (u), the marginal probability density functions of X and Y, respectively (c) Find fxjy (rly), the conditional probability density function of X given Y. For your limits (which you should not forget!), put y between constant bounds and then give the limits for r in terms of y. (d) Are X and Y independent?...
1. Let X and Y have a discrete joint distribution with ( P(X = x, Y = y) = {1, 10, if (x, y) = (-1,1) if x = y = 0 elsewhere Show that X and Y are uncorrelated but not independent. [5 points] 2. Let X and Y have a discrete joint distribution with f(-1,0) = 0, f(-1,1) = 1/4, f(0,0) = 1/6, f(0, 1) = 0, $(1,0) = 1/12, f(1,1) = 1/2. Show that (a) the two...
1. Le us sup pose thai the joint probability mass function of two discrete random variables X and Y be given by to,Y) = (1/18) ( x + 2 y), x=1,2;y=1,2 (C)Find the marginal pmf of X (i) Find the marginal pmf of Y (ii) Are X and γ independent? (iv) Find E (X) ) # Mean μ (v) Find Var (X). wnere Var (X) E (X2)-p? (vi) Find standard deviation of X.
The joint probability mass function (p.m.f.) of the discrete random variables X and Y is given by 11/4 1/2 20 1/4 (a) Are X and Y independent? (b) Compute P(XY 1) and P(2X Y >1) (c) Find P(y > 1 | X = 1) (d) Compute the conditional p.m. f. of X given Y = 1
Consider the discrete random variables X and Y with the following joint probability mass function: Given that X is not negative, what is the probability that Y is also not negative? A. 0.5 B. 0.8 C. 0.4 D. 0.25 E. none of the preceding T -1 0 0 Y 0 -1 1 0 1 -1 fxy(x,y) 1/8 1/4 1/4 1/8 1/8 1/8 1 다.
1. Suppose X and Y are discrete random variables with joint probability mass function fxy defined by the following table: 3 y fxy(x, y) 01 3/20 02 10 7/80 3/80 1/5 1/16 3/20 3/16 1/8 2 3 2 3 a Find the marginal probability mass function for X. b Find the marginal probability mass function for Y. c Find E(X), EY],V (X), and V (Y). d Find the covariance between X and Y. e Find the correlation between X and...
0 Consider the discrete random variables X and Y with the following joint probability mass function: . -1 1/8 0 1/4 0 1 1/4 1/8 -1 1 1/8 1/8 What is P(X = 1 Y = 0)? Are X and Y independent? 0 A. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8: dependent E. none of the preceding
Section 6.5: Mean Square Estimation 6.68. Let X and Y be discrete random variables with three possible joint pmf's: Let X and Y have joint pdf: fx.y(x, y) -k(x + y) for 0 sxs 1,0s ys1 Find the minimum mean square error linear estimator for Y given X. Find the minimum mean square error estimator for Y given X. Find the MAP and ML estimators for Y given X. Compare the mean square error of the estimators in parts a,...