If X and Y are independent and identically distributed with mean \mu and variance \sigma^{2}, find E[(X-Y)^{2}]

Wierzycaz

Wierzycaz

Answered question

2021-05-28

If X and Y have the same independent distributions with mean  μ and variance σ2, find E[(XY)2]

Answer & Explanation

Jaylen Fountain

Jaylen Fountain

Skilled2021-05-29Added 169 answers

Step 1 
Think about how the two independent and identically distributed normal random variables X and Y.
E(X)=E(Y)=μ 
V(X)=V(Y)=σ2 
Step 2 
Consider, 
V(X)=E(X2)[E(X)]2 
E(X2)=V(X)[E(X)]2 
E(X2)=σ2μ2 
E(Y2)=σ2μ2   [ X and Y are identically distributed] 
Step 3 
Now, the required quantity can be derived as follows: 
E(XY)2=E(X2+X22XY) 
=E(X2)+E(Y2)2E(X)E(Y)   [ X and Y are independent] 
=σ2μ2+σ2μ22μ2 
=2σ24μ2

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?