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1. Say we have four sided dice (sides of 1, 2, 3, and 4, and each side is equally likely). A pair of four sided dice are to be rolled. Let X denote the sum of the two numbers that show up, and let Y denote the absolute value of their difference. a. Compute the joint probability mass function of X and Y, f(x, y) = P(X = x, Y = y) (Hint: X can be 2,3,4,5,6,7,8 and Y can be 0,1,2,3). Create a table. b. Compute the marginal pmfs of X and Y. Create tables. c. Find the conditional pmf of X given Y=0. Create table. d. Compute the expectation of X, E(X) and the expectation of Y, E(Y). e. Compute E(XY). f. Compute the covariance of X and Y, cov(X,Y). g. Are X and Y independent? Why or why not.

1. Say we have four sided dice (sides of 1, 2, 3, and 4, and each side is equally likely). A pair of four sided dice are to be rolled. Let X denote the sum of the two numbers that show up, and let Y denote the absolute value of their difference. a. Compute the joint probability mass function of X and Y, f(x, y) = P(X = x, Y = y) (Hint: X can be 2,3,4,5,6,7,8 and Y can be 0,1,2,3). Create a table. b. Compute the marginal pmfs of X and Y. Create tables. c. Find the conditional pmf of X given Y=0. Create table. d. Compute the expectation of X, E(X) and the expectation of Y, E(Y). e. Compute E(XY). f. Compute the covariance of X and Y, cov(X,Y). g. Are X and Y independent? Why or why not.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Problem Statement:** 1. Say we have four-sided dice (sides of 1, 2, 3, and 4, and each side is equally likely). A pair of four-sided dice are to be rolled. Let \( X \) denote the sum of the two numbers that show up, and let \( Y \) denote the absolute value of their difference. a. Compute the joint probability mass function of \( X \) and \( Y \), \( f(x, y) = P(X = x, Y = y) \) (Hint: \( X \) can be 2, 3, 4, 5, 6, 7, 8 and \( Y \) can be 0, 1, 2, 3). Create a table. b. Compute the marginal pmfs of \( X \) and \( Y \). Create tables. c. Find the conditional pmf of \( X \) given \( Y=0 \). Create table. d. Compute the expectation of \( X \), \( E(X) \) and the expectation of \( Y \), \( E(Y) \). e. Compute \( E(XY) \). f. Compute the covariance of \( X \) and \( Y \), \( \text{cov}(X,Y) \). g. Are \( X \) and \( Y \) independent? Why or why not?
Transcribed Image Text:**Problem Statement:** 1. Say we have four-sided dice (sides of 1, 2, 3, and 4, and each side is equally likely). A pair of four-sided dice are to be rolled. Let \( X \) denote the sum of the two numbers that show up, and let \( Y \) denote the absolute value of their difference. a. Compute the joint probability mass function of \( X \) and \( Y \), \( f(x, y) = P(X = x, Y = y) \) (Hint: \( X \) can be 2, 3, 4, 5, 6, 7, 8 and \( Y \) can be 0, 1, 2, 3). Create a table. b. Compute the marginal pmfs of \( X \) and \( Y \). Create tables. c. Find the conditional pmf of \( X \) given \( Y=0 \). Create table. d. Compute the expectation of \( X \), \( E(X) \) and the expectation of \( Y \), \( E(Y) \). e. Compute \( E(XY) \). f. Compute the covariance of \( X \) and \( Y \), \( \text{cov}(X,Y) \). g. Are \( X \) and \( Y \) independent? Why or why not?
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