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A Bernoulli random variable is one that assumes only two

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer ISBN: 9780495110811 47

Solution for problem 3E Chapter 4

Mathematical Statistics with Applications | 7th Edition

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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Mathematical Statistics with Applications | 7th Edition

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Problem 3E

Problem 3E

A Bernoulli random variable is one that assumes only two values, 0 and 1 with p(1) = p and p(0) = 1 − p q.

a Sketch the corresponding distribution function.

b Show that this distribution function has the properties given in Theorem 4.1.

Reference

Step-by-Step Solution:
Step 1 of 3

Solution 3E

Step1 of 3:

Let us consider a random variable X it follows bernoulli distribution with parameter ‘p’.

And range from 0 and 1 with P(0) = p and P(1) = 1 - p

                                                                             = q.

Here our goal is:

a). We need to sketch the corresponding distribution function.

b). We need to Show that this distribution function has the properties given in Theorem 4.1.


Step2 of 3:

a).

The distribution of X is given by:

 

The graph of the corresponding distribution function is:


Step3 of 3:

b).

Let

The distribution function of p is 0 everywhere except 0 and 1 thus:

                       

     

 = 0

Similarly,

                           

                   

       

 = 1

Therefore F is a non-decreasing function of X:


 

Step 2 of 3

Chapter 4, Problem 3E is Solved
Step 3 of 3

Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

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A Bernoulli random variable is one that assumes only two