Problems with Gaussian distribution

[cooper607]

Homework Statement

consider this Gaussian distribution
p(x)=Ae^-(a(x-b)^2)

Homework Equations

use integration p(x)dx=1 to find out the value of A

The Attempt at a Solution

hi, i know about the gaussian distribution formula integration e^-alpha*x^2 = sqrt(pi/alpha)

now for this integration i just could not figure out what the alpha should be. as if i want to get the moderate Gaussian form i ended up with e^-x^2(a-2ba/x+b^2*a/x^2)

as i could not get rid of x in my alpha term , can i still integrate it with the gaussian formula?
if not , then how can i fix my alpha here containing no x terms?
regards

 

[Dick]

Homework Statement

consider this Gaussian distribution
p(x)=Ae^-(a(x-b)^2)

Homework Equations

use integration p(x)dx=1 to find out the value of A

The Attempt at a Solution

hi, i know about the gaussian distribution formula integration e^-alpha*x^2 = sqrt(pi/alpha)

now for this integration i just could not figure out what the alpha should be. as if i want to get the moderate Gaussian form i ended up with e^-x^2(a-2ba/x+b^2*a/x^2)

as i could not get rid of x in my alpha term , can i still integrate it with the gaussian formula?
if not , then how can i fix my alpha here containing no x terms?
regards

Do a change of variables, u=x-b. du=dx. Now integrate du instead of dx.

 

[cooper607]

wow! that helps.. thanks a lot