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...
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...
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.