# Expected value equation

1. Mar 11, 2014

### Samwise_geegee

1. The problem statement, all variables and given/known data
Let x and y be independent random variables with E[x]=1, E[y]=-1, var[x]=1/2, var[y]=2
Calculate E[(x+1)2(y-1)2]

2. Relevant equations

E[x]=1=μ
E[y]=-1=μ
var[x]=1/2 =E[(x-μ)2]
var[y]=2=E[(x-μ)2]

3. The attempt at a solution

Since x and y are independent,
E[(x+1)2(y-1)2]=E[(x+1)2]*E[(y-1)2]

var[x]=1/2=E[(x-1)2]

var[y]=2=E[(y+1)2

The signs in the equation I need to solve are throwing me off. I feel like I'm missing something simple. Any help is appreciated!

2. Mar 11, 2014

### Ray Vickson

Sometimes the easiest approach is to use the standard result
$$\text{Var}(Y) = E(Y^2) - (E Y)^2,$$
which is true for any random variable having finite mean and variance. (At some point in your life, you should prove it.) You can expand out $(Y-1)^2$ and go on from there.

3. Mar 11, 2014

### Samwise_geegee

Thanks Ray!

Thank you for the hint! Does this look right?

E[(x+1)2]*E[(y-1)2]

=(E[X2]+2E[X]+E[1])(E[Y2]-2E[Y]+E[1])

=(Var[X]+E[X]2+2E[X]+E[1])(Var[Y]+E[Y]2-2E[Y]+E[1])

=(.5+1+2+1)(2+1+1+1)=18

Last edited: Mar 11, 2014