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# Find the mean and variance for the following discrete ISBN: 9780321923271 41

## Solution for problem 1E Chapter 2.3

Probability and Statistical Inference | 9th Edition

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Problem 1E

Find the mean and variance for the following discrete distributions: Step-by-Step Solution:

Step 1 of 3 :

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

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

b)

f(x) = 1,                  x = 5

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

= 5 (1)

= 5

The mean of the distribution is 5.

Variance = E( ) - ( E(x) Where,  E( ) = (1)

= 25

then , Variance = E( ) - ( E(x) =25 - = 0

The variance of the distribution is 0.

Step 3 of 3

##### ISBN: 9780321923271

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Find the mean and variance for the following discrete

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