6. (20%) Consider two random variables X and Y with the joint PMF given in Table...
Problem 8.2 X Y Discrete random variables X, Y have joint pmf given in the table to the right, where X takes values in {1,2,3,4} and Y takes values in {1,2,3). 2 3 1 2 3 0. 100.3 0 0.2 0.1 0 0.05 0.1 0 0.1 0.05 (e) Compute the MAP estimate of X given the observation Y = 2. Compute the posterior probabiity of error of this estimate, given that Y = 2. (f) Compute the MMSE estimate of...
Random variables \(X\) and \(Y\) have joint probability mass function (PMF):\(P_{X, Y}\left(x_{k}, y_{j}\right)=P\left(X=x_{k}, Y=y_{j}\right)= \begin{cases}\frac{1}{20}\left|x_{k}+y_{j}\right|, & x_{k}=-1,0,1 ; y_{j}=-3,0,3 \\ 0, & \text { otherwise }\end{cases}\)(a) Find \(F_{X, Y}(x, y)\), the joint cumulative distribution function (CDF) of \(X\) and \(Y\). A graphical representation is sufficient: probably the best way to do this is to draw the \(x-y\) plane and label different regions with the value of \(F_{X, Y}(x, y)\) in that region.(b) Let \(Z=X^{2}+Y^{2}\). Find the probability mass function (PMF)...
12) Random variables X & Y have joint pmf given in the table. Y = 1 Y = 2 Y= 3 X = 1 0.3 0.1 0 X = 2 0.1 0.3 0.2 In problem (12), determine Var(X | Y = 3) a) 2.4 b) 2.0 c) 1.4 d) .8 e) 0
1. (Hint: This pmf should look familiar) Random variables X and Y have joint probability mass function (IPMI): otherwise. (a) Find Fx,y(x, y), the joint cumulative distribution function (CDF) of X and Y. A graphical repre- sentation is sufficient: probably the best way to do this is to draw the x - y plane and label different regions with the value of Fx,y(x, y) in that region. (b) Let Z = X2 + Y2. Find the probability mass function (PMF)...
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)...
12) Random variables X & Y have joint pmf given in the table. Y = 1 Y = 2 Y= 3 X = 1 0.3 0.1 0 X = 2 0.1 0.3 0.2 In problem (12), determine E(3Y + 1.2 | X < Y ) a) 9.0 b) 9.2 c) 9.5 d) 9.8 e) 10.0
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(Y|X). (c) Find the expected values of X and Y, E(X), E(Y). (d) Find the variances of X...
Comparing two densities. Joint density (a) for random variables X and Y is given by: fxy(x, y) = 6e-23-if 0 <y<I<0. Joint density (b) for random variables X and Y is given by: fxY(I, y) = 2e -2- if 0 <1,7 <00. Fill in the following chart and determine whether or not X and Y are independent for both densities (a) and (b). fx() fy(y) EX EY EXY Cou(X,Y) Independent?
asap plz The joint probability density function of random variables X and Y is given by, otherwise a. Find k b. Find the best (non-linear) minimum mean squared error (MMSE) estimator for Y given X-r. 20]
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.