Question

Q4. Find the mean and variance for the following distributions

1-Gamma distribution with α=2 and β= 3

2-Exponential distribution with β= 30

3-Chi squire distribution with v= 30

4-Beta distribution with α=2 and β= 3

Answer 1

Solution:

1) Let, X follows gamma distribution with parameters

Given

The pdf of gamma distribution is,

  

Ans: Mean = 6 and Variance=18

2) Let X follows exponential distribution with parameter

Given

The pdf is given by,

  

  

Ans: Mean=0.033 and Variance = 0.0011

3) Let X follows chi-square distribution with parameter v

Given: v=30

The pdf is given by,

Ans: Mean = 30 and Variance = 60

4) Let X follows beta distribution with parameter

The pdf is given by,

where, B() is beta function.

  

  

Ans: Mean=0.4, Variance=0.04