# Variance of square of random variable

1. Jun 20, 2011

### roflmao33

1. The problem statement, all variables and given/known data

Lets say I roll 2 fair dice and take the sum of the square of each dice. What formula will be the variance?

2. Relevant equations
var(x)=e(x^2)-e(x)^2

3. The attempt at a solution
For dice A;
E(A)=3.5
E(A^2)=91/6
^ same for dice B.

VAR(A^2+B^2)=E(A^4)-E(A^2)^2+E(B^4)-E(B^2)^2 ?

2. Jun 20, 2011

### lanedance

how did you get to that? I'd start from
$$var(A^2+B^2) = E((A^2+B^2)^2) - E((A^2+B^2))^2$$

and simplify from there, though you'll probably end up at a similar place you need to justify it

3. Jun 21, 2011

### roflmao33

well since i am throwing two different dice and squaring them, this means that they are independent, shouldnt I be able to use var(x+y)=var(x)+var(y)?

VAR(A^2+B^2)=E(A^4)-E(A^2)^2+E(B^4)-E(B^2)^2

4. Jun 21, 2011

### lanedance

yep, you just need to mention your assumptions, you can also say the expectation values will be the same for A & B