1. Consider two discrete random variables, X and Y with marginal pmf's fx(x) and fy (y). Come up with an example for which the two random variables have different probability distributions, but the same means, i.e. fx(x) # fy (x) for at least one value of x, but E [X] = E [Y]. Keep your example as simple as possible. Do they have the same variance? In at most 5 sentences, discuss why this shows that the probability distribution contains more information about a random variable than its mean.

1. Consider two discrete random variables, X and Y with marginal pmf's fx(x) and fy (y). Come up with an example for which the two random variables have different probability distributions, but the same means, i.e. fx(x) # fy (x) for at least one value of x, but E [X] = E [Y]. Keep your example as simple as possible. Do they have the same variance? In at most 5 sentences, discuss why this shows that the probability distribution contains more information about a random variable than its mean.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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