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Let X~ N(2,1), Y~ N(-1,4), and cov(X, Y) = 2. a. Find E[X-Y] b. Find the correlation coefficient p(X,Y) c. Find Var[X - Y]. 3 d. Suppose in addition to the above conditions, we have that X - Y is a normal random variable. What is P(X - Y> 0)?

Let X~ N(2,1), Y~ N(-1,4), and cov(X, Y) = 2. a. Find E[X-Y] b. Find the correlation coefficient p(X,Y) c. Find Var[X - Y]. 3 d. Suppose in addition to the above conditions, we have that X - Y is a normal random variable. What is P(X - Y> 0)?

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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Let X~ N(2,1), Y ~ N(-1,4), and cov(X, Y) = 2. a. Find E[X-Y] b. Find the correlation coefficient p(X, Y) c. Find Var[X - Y]. d. Suppose in addition to the above conditions, we have that X - Y is a normal random variable. What is P(X - Y > 0)?
Transcribed Image Text:Let X~ N(2,1), Y ~ N(-1,4), and cov(X, Y) = 2. a. Find E[X-Y] b. Find the correlation coefficient p(X, Y) c. Find Var[X - Y]. d. Suppose in addition to the above conditions, we have that X - Y is a normal random variable. What is P(X - Y > 0)?
Expert Solution
Step 1: Given information

We have given that:

 X tilde N open parentheses 2 comma space 1 close parentheses , Y tilde N open parentheses negative 1 comma space 4 close parentheses,  and c o v open parentheses X comma space Y close parentheses equals 2

i.e. mu subscript x equals 2,  sigma subscript x superscript 2 equals 1 and 

     mu subscript y equals negative 1,  sigma subscript y superscript 2 equals 4

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