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Find the mean and variance for the following discrete

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 1E Chapter 2.3

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 1E

Problem 1E

Find the mean and variance for the following discrete distributions:

Step-by-Step Solution:

Answer :

Step 1 of 3 :

The claim is to find the mean and variance for the given,

  1. f(x) = ,                 x = 5, 10, 15, 20, 25.
  2. f(x) = 1,                  x = 5
  3. f(x) = ,             x = 1, 2, 3.

             The mean is E(x) = x f(x)

                                          = 5 () + 10  ()   +  15  ()  + 20  ()   +  25 ()

                                          = 1  +  2  +  3  +  4  +  5

                                          = 15

The mean of the distribution is 15.

Variance = E() - ( E(x)

     

Where,  E() =   () +   ()   +    ()  +   ()   +   ()

                                          = 5 + 20 + 45 + 80 + 125

                                          = 275

then , Variance = E() - ( E(x)

                        = 275  -  

                         = 50

The variance of the distribution is 50.


Step 2 of 3

Chapter 2.3, Problem 1E is Solved
Step 3 of 3

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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Find the mean and variance for the following discrete