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What holds for PY |X(y|x) and PX|Y (x|y) if the random variables X and Y are independent?

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

What holds for PY |X(y|x) and PX|Y (x|y) if the random variables X and Y are independent?
3. It holds true that
EX[(x − 2)2] = EX[x2] − a · EX[x] + b.
What are a and b?
4. Prove that the maximum likelihood decision is maximum a posteriori, too, if PS(s)
is constant.

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