use the second definition of conditional expectations Let X be a square-integrable a random variables. Starting from the projection definition of a conditional 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.

use the second definition of conditional expectations Let X be a square-integrable a random variables. Starting from the projection definition of a conditional 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.

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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Question

use the second definition of conditional expectations

Let X be a square-integrable a random variables. Starting from the projection definition of a
conditional 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.

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