In this problem we will explore the properties of the Probability Mass Function (PMF). Let X be a discrete random variable, and px (r) its PMF. (a) Recall that px (x): R→ [0, 1] (the PMF is a function from the real numbers to [0,1]), and that R is an uncountable set. Why then, in words, can we still use the PMF to characterize a discrete random variable? (b) Formalize your answer in part (a) mathematically by proving the statement: {ER | px(x) 0} is a countable set. (c) In words, explain why necessarily E, Px(x) = 1. (d) Prove the statement in part (c) mathematically, using the fact that P() = 1.

In this problem we will explore the properties of the Probability Mass Function (PMF). Let X be a discrete random variable, and px (r) its PMF. (a) Recall that px (x): R→ [0, 1] (the PMF is a function from the real numbers to [0,1]), and that R is an uncountable set. Why then, in words, can we still use the PMF to characterize a discrete random variable? (b) Formalize your answer in part (a) mathematically by proving the statement: {ER | px(x) 0} is a countable set. (c) In words, explain why necessarily E, Px(x) = 1. (d) Prove the statement in part (c) mathematically, using the fact that P() = 1.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.3: Binomial Probability

Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...

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