Q1. [4+2+4 marks] Consider the following joint probability distribution fxy(x, y). 2 4 0.05 0.1 0,05...
4. (20 points) Suppose the joint distribution of X and Y is: fxy(x, y) 1 0 1 2 3 0.04 0.06 0.01 0.00 0.13 0.13 0.02 0.12 0.04 0.06 0.00 0.11 0.07 0.10 0.06 (a) (4 points) Find the marginal distributions of X and Y. (b) (4 points) Given X = 3, what is the probability that random variable Y is at most 2?. (c) (4 points) Are random variables X and Y independent? Why or why not? (d) (4...
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)
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY). 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3...
ka (3) [6 pts] X and Y are discrete random variables with the following joint distribution: 14 22 30 065 102 0.05 0.10 0.03 0.01 Value ofX 50.17 0.15 0.05 0.02 0.01 8 0.02 0.03 0.15 0.10 (a) Calculate the probability distribution, mean, and variance of Y (b) Calculate the prohability distribution, mea, and variane of Y given X (c) Calculate the covariance and correlation between X and Y 8
Question 4: Let X and Y be two discrete random variables with the following joint probability distribution (mass) function Pxy(x, y): a) Complete the following probability table: Y 2 f(x)=P(X=x) 1 3 4 0 0 0.08 0.06 0.05 0.02 0.07 0.08 0.06 0.12 0.05 0.03 0.06 0.05 0.04 0.03 0.01 0.02 0.03 0.04 2 3 foy)=P(Y=y) 0.03 b) What is P(X s 2 and YS 3)? c) Find the marginal probability distribution (mass) function of X; [f(x)]. d) Find the...
Please provide correct answer (Very Important) Consider the following joint probability distribution: y fxY (x, y) -1.0 -3 1/8 -0.4 -1 1/4 0. 4 1 1/16 1. 0 3 9/16 Determine the following: (a) Conditional probability distribution of Y given that X = 1 fyll(y) = for y = (b) Conditional probability distribution of X given that Y = 1 fxli (x) = for x = (c) E(X|Y = 1) = (d) Are X and Y independent?
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.
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...
Given the following joint distribution of two random variables X and Y (a) Compute marginal distribution PX(x) (b) Compute marginal distribution PY(y) (c) What is the conditional probability P(Y | X = 2)? 20.10 0.05 0.15 0.10 0.10 4 0.04 0.02 0.06 0.04 0.04 6 0.04 0.02 0.06 0.06 0.02 8 0.02 0.01 0.03 0 0.04