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A First Course in Probability
Found in: Page 361
A First Course in Probability

A First Course in Probability

Book edition 9th
Author(s) Sheldon M. Ross
Pages 432 pages
ISBN 9780321794772

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Short Answer

Prove that E[g(X)YX]=g(X)E[YX].

We prove that, E[g(X)YX]=g(X)E[YX]

See the step by step solution

Step by Step Solution

Step 1: Given information

Given in the question that, we have to prove that E[g(X)YX]=g(X)E[YX]

Step 2: Explanation

Because of the clarity, suppose that X and Y are continuous random variables with its density functions. Take any x suppfX. We have that


But, we have that


So the integral becomes


Which is equal to


Since the relation hold for every xsuppf, we end up with


Step 3: Final answer

We prove that, E[g(X)YX]=g(X)E[YX]

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