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Let Y be a binomial random variable with n = 1 and success

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

Solution for problem 4E 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 4E

Problem 4E

Let Y be a binomial random variable with n = 1 and success probability p.

a Find the probability and distribution function for Y .

b Compare the distribution function from part (a) with that in Exercise 4.3(a). What do you conclude?

Reference

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:

Solution:

Step 1 of 2:

Let Y be a Binomial random variable with n = 1, p be the probability of success and q be the probability of failure

The claim is to find the probability and distribution function for Y.

The probability for Y is given by

P(Y = K) =  

we have n = 1

Then, P(Y = K) =

If k =o, P(Y = K) = 1 - p

If k =1, P(Y = K) =  p

The probability function of Y is

 

Hence, the distribution function is


Step 2 of 2

Chapter 4, Problem 4E is Solved
Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. The full step-by-step solution to problem: 4E from chapter: 4 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. Since the solution to 4E from 4 chapter was answered, more than 298 students have viewed the full step-by-step answer. This full solution covers the following key subjects: distribution, function, Probability, reference, variable. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. The answer to “Let Y be a binomial random variable with n = 1 and success probability p.a Find the probability and distribution function for Y .b Compare the distribution function from part (a) with that in Exercise 4.3(a). What do you conclude?ReferenceA 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” is broken down into a number of easy to follow steps, and 82 words.

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Let Y be a binomial random variable with n = 1 and success