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A random variable X has a binomial distribution, and a

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 9E Chapter 4.3

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 9E

A random variable \(X\) has a binomial distribution, and a random variable \(Y\) has a Poisson distribution. Both \(X\) and \(Y\) have means equal to 3. Is it possible to determine which random variable has the larger variance? Choose one of the following answers:

i. Yes, \(X\) has the larger variance.

ii. Yes, \(Y\) has the larger variance.

iii. No, we need to know the number of trials, \(n\), for \(X\).

iv. No, we need to know the success probability, \(p\), for\(X\).

v. No, we need to know the value of \(\lambda\) for \(Y\) .

Equation Transcription:

Text Transcription:

 

X

Y

n

p

lambda

Step-by-Step Solution:

Solution

 

Step 1 of 2

Here XB(n,p)

The mean of the binomial distribution is ‘np’=3

The variance of the binomial distribution is ‘np(1-p)’<3

Because 1-p<0


Step 2 of 2

Chapter 4.3, Problem 9E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Since the solution to 9E from 4.3 chapter was answered, more than 404 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The full step-by-step solution to problem: 9E from chapter: 4.3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This full solution covers the following key subjects: random, variance, variable, larger, yes. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The answer to “?A random variable \(X\) has a binomial distribution, and a random variable \(Y\) has a Poisson distribution. Both \(X\) and \(Y\) have means equal to 3. Is it possible to determine which random variable has the larger variance? Choose one of the following answers:i. Yes, \(X\) has the larger variance.ii. Yes, \(Y\) has the larger variance.iii. No, we need to know the number of trials, \(n\), for \(X\).iv. No, we need to know the success probability, \(p\), for\(X\).v. No, we need to know the value of \(\lambda\) for \(Y\) .Equation Transcription:Text Transcription: X Ynplambda” is broken down into a number of easy to follow steps, and 94 words.

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A random variable X has a binomial distribution, and a