Let X be a square-integrable a random variables. Starting from the projection definition of aconditional expectation, prove that E[X]{0, 2}] = E[X], E[X]o(X)] = X, and E[g(X)|o(X)] = g(X),where g is a Borel function and E[g²(X)] < x.

Given that X be a square-integrable random variables.

Answered: Let X be a square-integrable a random…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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Let X be a square-integrable a random variables. Starting from the projection definition of a conditional expectation, prove that E[X]{Ø, S}] = E[X], E[X]o(X)] = X, and E[g(X)o(X)] = g(X), where g is a Borel function and E[g²(X)] < x.