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Suppose that X takes on one of the values 0, 1, and 2. If

A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross ISBN: 9780321794772 63

Solution for problem 2STE Chapter 4

A First Course in Probability | 9th Edition

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A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross

A First Course in Probability | 9th Edition

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Problem 2STE

Problem 2STE

Suppose that X takes on one of the values 0, 1, and 2. If for some constant c,P{X = i} = cP{X = i− 1}, i = 1, 2, find E[X].

Step-by-Step Solution:

Answer

Step 1 of 1

(a)

Suppose that  takes on one of the values  If for some constant  

We are asked to find

We have given

This relationship implies that  where

Because these probabilities sum to 1, we can write,

We know the expectation of a random variable

Hence is


Step 2 of 1

Chapter 4, Problem 2STE is Solved
Textbook: A First Course in Probability
Edition: 9
Author: Sheldon Ross
ISBN: 9780321794772

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Suppose that X takes on one of the values 0, 1, and 2. If