Problem 2. (a) Consider a random variable X E {1,2,...,n}. Show that (i) µ(X) >0 (ii) o(X) > 0 for all possible probability distributions p = (px(1), px(2), px (3), ...,px (n)). (b) Consider Y ={±1,±2,...,±n/2}. State a probability distribution that satisfies µ(Y) < 0.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 2.
(a) Consider a random variable X E {1,2,...,n}. Show that
(i) µ(X) >0
(ii) o(X) > 0
for all possible probability distributions p = (px(1), px(2), px (3), ...,px (n)).
(b) Consider Y ={±1,±2,...,±n/2}. State a probability distribution that satisfies µ(Y) < 0.
Transcribed Image Text:Problem 2. (a) Consider a random variable X E {1,2,...,n}. Show that (i) µ(X) >0 (ii) o(X) > 0 for all possible probability distributions p = (px(1), px(2), px (3), ...,px (n)). (b) Consider Y ={±1,±2,...,±n/2}. State a probability distribution that satisfies µ(Y) < 0.
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