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# ISI MStat PSB 2008 Problem 7 | Finding the Distribution of a Random Variable This is a very beautiful sample problem from ISI MStat PSB 2008 Problem 7 based on finding the distribution of a random variable . Let's give it a try !!

## Problem- ISI MStat PSB 2008 Problem 7

Let and be exponential random variables with parameters 1 and 2 respectively. Another random variable is defined as follows.

A coin, with probability p of Heads (and probability 1-p of Tails) is
tossed. Define by Find ### Prerequisites

Cumulative Distribution Function

Exponential Distribution

## Solution :

Let , be the CDF for i=X,Y, Z then we have , = = Therefore pdf of Z is given by , where are pdf of X,Y respectively .

So , ## Food For Thought

Find the the distribution function of and then find ## Subscribe to Cheenta at Youtube

This is a very beautiful sample problem from ISI MStat PSB 2008 Problem 7 based on finding the distribution of a random variable . Let's give it a try !!

## Problem- ISI MStat PSB 2008 Problem 7

Let and be exponential random variables with parameters 1 and 2 respectively. Another random variable is defined as follows.

A coin, with probability p of Heads (and probability 1-p of Tails) is
tossed. Define by Find ### Prerequisites

Cumulative Distribution Function

Exponential Distribution

## Solution :

Let , be the CDF for i=X,Y, Z then we have , = = Therefore pdf of Z is given by , where are pdf of X,Y respectively .

So , ## Food For Thought

Find the the distribution function of and then find ## Subscribe to Cheenta at Youtube

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