+ Post New Thread

Results 1 to 3 of 3

- 13th April 2011, 20:13 #1

- Join Date
- Sep 2010
- Posts
- 69
- Helped
- 2 / 2
- Points
- 1,065
- Level
- 7

## variance of the product of two random variables

If I have two RV's X and Y (which are not necessarily independent), what would be the approach to find the variance of their product assuming that I know variances of X and Y, i.e. if Z=XY, what is var(Z)?

I searched on google and found some suggestions, but most of them were based on the assumption that X and Y are independent. What would be a more general solution?

Thanks a lot.

- 13th April 2011, 20:13

- 14th April 2011, 12:33 #2

- Join Date
- Nov 2010
- Location
- Germany
- Posts
- 36
- Helped
- 2 / 2
- Points
- 531
- Level
- 4

## Re: variance of the product of two random variables

If there exists corelation between X and Y, then finding the variance of Z becomes slightly more complicated due to the requirement of knowing the covariance of X and Y.

Syntax: [] = covariance, <> = variance, "" = Mean, () = Normal Paranthese

<Z> = [XY] . ( [XY] + 2."X"."Y" ) + <X>.<Y> + <X>("Y"^2) + <Y>("X"^2)

Hope it helps.

{Btw, it can be simplified into just 3 terms: <Z> = "XY"^2 + ("XX"."YY") - (2 . ("X"^2) . ("Y"^2)), but as I said you need to take covariance into account. }

- 14th April 2011, 12:33

- 15th April 2011, 13:35 #3

- Join Date
- Apr 2011
- Location
- India
- Posts
- 55
- Helped
- 6 / 6
- Points
- 528
- Level
- 4

## Re: variance of the product of two random variables

If you want to develop considerable knowledge, read functions of random variables from Papoulius book.

+ Post New Thread

Please login

#### LinkBacks (?)

- 13th July 2012, 15:58
- 13th July 2012, 12:05