1. Assume Y=1+X+u, where X, Y, and u=v+Xare r.v.S, v is independent ofX; E(v)=0, Var(v)=1, ECX) 1, and Var(X) 2 1) Calculate E(uX=1), E(Y]X=1), E(u|X=2), E(Y]X=2}, E(uX), ECY]X), E(u) and E(Y) 2) Calculate Var(u|X=1), Var(Y\X=1), Var(u|X=2), Var(Y]X=2), Var(u|X), VarYX),

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 12EQ
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Part 1 and 2

1. Assume Y=1+X+u, where X, Y, and u=v+Xare r.v.S, v is independent ofX; E(v)=0,
Var(v)=1, ECX) 1, and Var(X) 2
1) Calculate E(uX=1), E(Y]X=1), E(u|X=2), E(Y]X=2}, E(uX), ECY]X), E(u) and
E(Y)
2) Calculate Var(u|X=1), Var(Y\X=1), Var(u|X=2), Var(Y]X=2), Var(u|X),
VarYX),
Transcribed Image Text:1. Assume Y=1+X+u, where X, Y, and u=v+Xare r.v.S, v is independent ofX; E(v)=0, Var(v)=1, ECX) 1, and Var(X) 2 1) Calculate E(uX=1), E(Y]X=1), E(u|X=2), E(Y]X=2}, E(uX), ECY]X), E(u) and E(Y) 2) Calculate Var(u|X=1), Var(Y\X=1), Var(u|X=2), Var(Y]X=2), Var(u|X), VarYX),
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