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The space of integrable random variable is L'. Recall from Definition L.27 that a random variable defined on a probability space (N, F, P) is integrable if E[|X|] < 0o. The space L'(N,F,P) i defined to be the space of integrable random variables.

The space of integrable random variable is L'. Recall from Definition L.27 that a random variable defined on a probability space (N, F, P) is integrable if E[|X|] < 0o. The space L'(N,F,P) i defined to be the space of integrable random variables.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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2.16. The space of integrable random variable is L'. Recall from Definition 1.27 that |a random variable defined on a probability space (0, F, P) is integrable if E[|X|] < o. The space I'(0,F,P) is defined to be the space of integrable random variables. Show that L'(N, F,P) is a linear space; that is, if X, Y E L', then aX + bY EL' for any a, b eR. What is the zero vector? Verify that ||X||1 = E[[X]] is a norm for L'.
Transcribed Image Text:2.16. The space of integrable random variable is L'. Recall from Definition 1.27 that |a random variable defined on a probability space (0, F, P) is integrable if E[|X|] < o. The space I'(0,F,P) is defined to be the space of integrable random variables. Show that L'(N, F,P) is a linear space; that is, if X, Y E L', then aX + bY EL' for any a, b eR. What is the zero vector? Verify that ||X||1 = E[[X]] is a norm for L'.
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