An Alternative Variance Formula

  • I
  • Thread starter mathman
  • Start date
  • #1
mathman
Science Advisor
7,839
439

Summary:

Interesting formula for variance

Main Question or Discussion Point

I derived (trivially) an expression for the variance of a random variable (which I had never noticed before). Let ##X## be a random variable with cdf ##F(x)## then (assuming finite second moment). ##Var(X)=\frac{1}{2}\int\int (x-y)^2dF(x)dF(y)##.

Is this expression of any use?
 
Last edited:

Answers and Replies

  • #2
FactChecker
Science Advisor
Gold Member
5,703
2,110
It looks so much more complicated than other equations that I can't think of a use for it.
This seems much more convenient: ##Var(X) = \int {X^2}dF - (\int X dF)^2##

PS. I have not taken time to verify your formula. I do not see it immediately.
 
  • #3
mathman
Science Advisor
7,839
439
It looks so much more complicated than other equations that I can't think of a use for it.
This seems much more convenient: ##Var(X) = \int {X^2}dF - (\int X dF)^2##

PS. I have not taken time to verify your formula. I do not see it immediately.
##(x-y)^2=x^2+y^2-2xy## gives the usual formula.
 
  • Like
Likes FactChecker

Related Threads on An Alternative Variance Formula

  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
2
Views
222
Replies
13
Views
9K
  • Last Post
Replies
4
Views
21K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
18
Views
5K
  • Last Post
Replies
2
Views
2K
Top