Gaussian integral

  • Thread starter jaobyccdee
  • Start date
  • #1
33
0
How to show that the variance of the gaussian distribution using the probability function? I don't know how to solve for ∫r^2 Exp(-2r^2/2c^2) dr .
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,260
619
Use integration by parts and a substitution. It's really closely related to the integral of Exp(r^2).
 
Last edited:
  • #3
33
0
I tried it. The probability function is 1/(sqrt(2Pi c^2)) * Exp[-r^2/2c] When integrate it from -infinity to infinity, the Exp[r^2] makes everything 0. But we are trying to proof that it's equal to c.
 
  • #4
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728
I tried it. The probability function is 1/(sqrt(2Pi c^2)) * Exp[-r^2/2c] When integrate it from -infinity to infinity, the Exp[r^2] makes everything 0. But we are trying to proof that it's equal to c.
Absolutely not: the integral of exp(-x^2) for x going from - infinity to + infinity is a finite, positive value (it is the area under the curve of the graph y = exp(-x^2)); furthermore, this integral can be found everywhere in books and web pages; I will let you find it.

Anyway, you need to find an integral of the form int_{x=-inf..inf} x^2*exp(-x^2) dx, which is obtained from yours by an appropriate change of variables, etc. Integrate by parts, setting u = x and dv = x*exp(-x^2) dx.

RGV
 
  • #5
33
0
thx!!:)
 

Related Threads on Gaussian integral

  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
12
Views
1K
  • Last Post
Replies
4
Views
6K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
2
Views
668
  • Last Post
Replies
8
Views
9K
  • Last Post
Replies
9
Views
9K
Replies
12
Views
6K
Top