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
here P(X<Y)=P(X=1,Y=2)+P(X=1,Y=3)+P(X=2,Y=3)=0.1+0+0.2=0.3
hence E( 3Y + 1.2 | X < Y ) =(3*2+1.2)*(0.1/0.3)+(3*3+1.2)*(0.2/0.3)=9.2
option B is correct
12) Random variables X & Y have joint pmf given in the table. Y = 1...
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
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...
Assume that X and Y are discrete random variables having the joint pmf given by the following chart Y 0 1 2 0 0.1 0.1 0.3 X 1 0.3 0.1 0.1 a. Find the probability that Y is greater than X. b. Find the covariance between X and Y.
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.
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
2. Let X and X be two random variables with the following joint PMF Yix 2 0 2 0 0.1 0.05 0.05 0.15 0.1 0.05 0.1 0.05 0.05 0.05 4 0.05 0.05 0.02 0.1 0.03 total 0.2 0.2 0.12 0.3 0.18 total 0.45 0.3 0.25 1 1) Find E[X] and E[Y]. (10 points) 2) What is the covariance of X and Y? (20 points) 3) Are X and Y independent? Explain. (10 points)
13. Let X and Y be rv's whose joint PMF is given by: Y=1 2 3 X=0 0.2 0.1 0 1 0.1 0.3 0. 2 . 0 0 0.3 Compute the covariance and correlation matrix of the random vector (X,Y).
1. The joint pmf of X and Y is given by the table 20.1 0.1 0.1 0.1 50.2 0 00 60.1 0.1 0.1 0.1 (a) Determine the (marginal) pmf of X and of Y (b) Are X and Y independent? (c) Calculate Cov(X, Y).
Questionl The random variable X and Y have the following joint probability mass function: 0.14 0.27 0.2 0.1 0.03 0.15 0.1 a) Determine the b) Find P(X-Y>2). c) Find PX s3|Y20) d) Determine E(XY) e) Determine E(X) and E(Y). f) Are X and Y independent? marginal pmf for X and Y. Question 2 Let X and Y be independent random variables with pdf 2-y 0sxS 2 f(x)- f(p)- 0, otherwise 0, otherwise a) b) Find E(XY). Find Var (2X +...
. Suppose we have the following joint distribution for random variables X and Y 2 0.1 0.2 0.1 4 0 0.3 0.1 6 0 0 0.2 (a) Find p(X). That is find the marginal distribution of X. (b) Find p(Y). That is find the marginal distribution of Y (c) Find the distribution of X conditional on Y = 3. (d) Find the distribution of X conditional on Y 2 (e) Are X and Y independent? You should be able to...