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 randomvariable. 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)?