This is a very beautiful sample problem from ISI MStat PSB 2006 Problem 6 based on counting principle . Let's give it a try !!
Let be i.i.d. continuous random variables. For i=1,2, define
as
Find the mean and variance of .
Basic Counting Principle
Probability
Continuous random variable
Now , as there are only two cases either
or
.
Similarly ,
So,
.
Similarly ,
( as there are 3! possible arrangements of
keeping inequalities fixed .
Therefore ,
Find the same under the condition that are iid poission random variables .
This is a very beautiful sample problem from ISI MStat PSB 2006 Problem 6 based on counting principle . Let's give it a try !!
Let be i.i.d. continuous random variables. For i=1,2, define
as
Find the mean and variance of .
Basic Counting Principle
Probability
Continuous random variable
Now , as there are only two cases either
or
.
Similarly ,
So,
.
Similarly ,
( as there are 3! possible arrangements of
keeping inequalities fixed .
Therefore ,
Find the same under the condition that are iid poission random variables .