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# Probability density 2-sphere change variables watch

1. (**** i apologise I can not seem to edit the title, it is not a geometric distribution ! )

q13)

I have probabilty density

The question is let be measured with respect to the z-axis, find the probability that the particle lies between and ?

2. Relevant equations
see above

3. The attempt at a solution

My method:

=

This is wrong by a minus sign and the solutions instead do:

? (the '...' being the integration over . )

MY QUESTION:

I don't understand where or why the modulus signs come from in the transformation variables : ?

Many thanks
2. (Original post by xfootiecrazeesarax)
(**** i apologise I can not seem to edit the title, it is not a geometric distribution ! )

q13)

I have probabilty density

The question is let be measured with respect to the z-axis, find the probability that the particle lies between and ?

2. Relevant equations
see above

3. The attempt at a solution

My method:

=

This is wrong by a minus sign and the solutions instead do:

? (the '...' being the integration over . )

MY QUESTION:

I don't understand where or why the modulus signs come from in the transformation variables : ?

Many thanks
I'm confused as to what exactly your working is, or what is the working of the given solution. Can you put up a picture or your full working and the solution that you have.

If I had to guess, I'd say that they are taking the modulus of a 1D Jacobian i.e. they are trying to treat a 1D case consistently with a 2D case, or something along those lines.
3. (Original post by xfootiecrazeesarax)
..
If , then your limits are going to be reversed after the substitution, creating an additional minus sign.

e.g. , setting z = \cos \theta gives the integral

, which is the same as .

(atsruser is also correct that in general you want to use the modulus of the Jacobean)

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