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Let Y, X be independent and square-integrable random variables, and let Z = max(Y + X, 0) Show that if 1. E(X) < 0 and Y and Z are iid, then Var(X) 2 |E(X)| E(Y) = E(Z) < 2. E(X) > 0 and E(Y) > 0, then E(Z) > E(Y)+ E(X)

Let Y, X be independent and square-integrable random variables, and let Z = max(Y + X, 0) Show that if 1. E(X) < 0 and Y and Z are iid, then Var(X) 2 |E(X)| E(Y) = E(Z) < 2. E(X) > 0 and E(Y) > 0, then E(Z) > E(Y)+ E(X)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 13EQ
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Let Y, X be independent and square-integrable random variables, and let Z = max(Y +X , 0) Show that if 1. E(X) <0 and Y and Z are iid, then Var(X) 2 |E(X)| E(Y) = E(Z) < 2. E(X) > 0 and E(Y) > 0, then E(Ζ) E(Y) + Ε(X) Hint: Define T = max(-(Y+ X), 0) and use the fact that (Z .T = 0).
Transcribed Image Text:Let Y, X be independent and square-integrable random variables, and let Z = max(Y +X , 0) Show that if 1. E(X) <0 and Y and Z are iid, then Var(X) 2 |E(X)| E(Y) = E(Z) < 2. E(X) > 0 and E(Y) > 0, then E(Ζ) E(Y) + Ε(X) Hint: Define T = max(-(Y+ X), 0) and use the fact that (Z .T = 0).
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