This is a very beautiful sample problem from ISI MStat PSB 2008 Problem 2 based on definite integral as the limit of the Riemann sum . Let's give it a try !!
For let
Find .
Integration
Gamma function
Definite integral as the limit of the Riemann sum
, this can be written you may see in details Definite integral as the limit of the Riemann sum .
Therefore , ----(1) , let
Substituting we get ,
Statistical Insight
Let i.e X is a standard normal random variable then,
called folded Normal has pdf
. (Verify!)
So, from (1) we can say that
( As that a PDF of folded Normal distribution ) .
Find the same when .
This is a very beautiful sample problem from ISI MStat PSB 2008 Problem 2 based on definite integral as the limit of the Riemann sum . Let's give it a try !!
For let
Find .
Integration
Gamma function
Definite integral as the limit of the Riemann sum
, this can be written you may see in details Definite integral as the limit of the Riemann sum .
Therefore , ----(1) , let
Substituting we get ,
Statistical Insight
Let i.e X is a standard normal random variable then,
called folded Normal has pdf
. (Verify!)
So, from (1) we can say that
( As that a PDF of folded Normal distribution ) .
Find the same when .