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# ISI MStat PSB 2008 Problem 2 | Definite integral as the limit of the Riemann sum 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 !!

## Problem- ISI MStat PSB 2008 Problem 2

For let Find .

### Prerequisites

Integration

Gamma function

Definite integral as the limit of the Riemann sum

## Solution : , 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 ) .

## Food For Thought

Find the same when .

## Subscribe to Cheenta at Youtube

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 !!

## Problem- ISI MStat PSB 2008 Problem 2

For let Find .

### Prerequisites

Integration

Gamma function

Definite integral as the limit of the Riemann sum

## Solution : , 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 ) .

## Food For Thought

Find the same when .

## Subscribe to Cheenta at Youtube

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