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)?
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)?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1. Let \( X \sim N(2,1) \), \( Y \sim N(-1,4) \), and \( \text{cov}(X,Y) = 2 \).
a. Find \( E[X - Y] \)
b. Find the correlation coefficient \( \rho(X, Y) \)
c. Find \( \text{Var}[X - Y] \)
d. Suppose in addition to the above conditions, we have that \( X - Y \) is a normal random variable. What is \( P(X - Y > 0) \)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa86feb48-aed4-4133-a748-653f8a12a813%2F158c71dd-0a35-419a-8e10-2d0bebe72c40%2F0151ui9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Let \( X \sim N(2,1) \), \( Y \sim N(-1,4) \), and \( \text{cov}(X,Y) = 2 \).
a. Find \( E[X - Y] \)
b. Find the correlation coefficient \( \rho(X, Y) \)
c. Find \( \text{Var}[X - Y] \)
d. Suppose in addition to the above conditions, we have that \( X - Y \) is a normal random variable. What is \( P(X - Y > 0) \)?
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