How can I get Var(XY) when X,Y are independent?

I am mainly interested in the method of getting a formula for this than the formula itself, because my book has a lot of these formulas but I don't want to blindly memorize them...

Printable View

- December 17th 2009, 10:05 AMpaulrbVariance of the product of two independent variables
How can I get Var(XY) when X,Y are independent?

I am mainly interested in the method of getting a formula for this than the formula itself, because my book has a lot of these formulas but I don't want to blindly memorize them... - December 17th 2009, 12:20 PMnovice
I will show you the process, but you need to do the rest.

The definition of variance with a single random variable is .

After expanding and eliminating you will get

For two variable, you substiute X with XY, it becomes

----eq(1)

where and --------------------eq(2)

When X and Y are independent ------eq(3)

Substitute eq(2) and eq(3) into eq(1). You should get the final form you find in you book.