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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Answered: Let X~ N(2,1), Y~ N(-1,4), and cov(X,Y)…

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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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)?