Here's the problem that I am having.

Let X and Y be random variables with E(X)=1, E(Y)= 4 Var(X)= 4 Var(Y)=6 p=1/2. Find mean and variance of Z= 3X-2Y.

I found the mean. I just need help finding Var(Z). Please help me out. Thanks.

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- Aug 3rd 2008, 08:05 AMhelium0204Issues With Expectations
Here's the problem that I am having.

Let X and Y be random variables with E(X)=1, E(Y)= 4 Var(X)= 4 Var(Y)=6 p=1/2. Find mean and variance of Z= 3X-2Y.

I found the mean. I just need help finding Var(Z). Please help me out. Thanks. - Aug 3rd 2008, 12:57 PMMoo
Hello,

For this, you have to remember that the mean is a linear function, that is to say E(aX+bY)=aE(X)+bE(Y)

For the variance, the formula is : var(aX+bY)=a^2 var(X)+b^2 var(Y), assuming that X and Y are independent. Otherwise you will need more information.

You can prove this formula with the definition of the variance that includes the mean :

var(X)=E(X^2)

and var(X+Y)=var(X)+var(Y) if X and Y are independent.

Edit : What is p ??? - Aug 3rd 2008, 01:52 PMhelium0204
- Aug 3rd 2008, 03:48 PMMoo
Okay

Use the fact that the correlation coefficient is equal to :

$\displaystyle \frac{\text{covariance}(X,Y)}{\sigma_X \cdot \sigma_Y}$, where $\displaystyle \sigma$ represents the standard deviation, that is to say $\displaystyle \sqrt{\text{variance}}$.

Then, use the following formula : var(X+Y)=var(X)+var(Y)+2 cov(X,Y), where cov is the covariance