Cauchy distribuation and maths help

Hello i have this question that i am struggling to answer regarding changing variables, i really dont know how to do it :(

A gun fires at random in the angular range −π/2 < θ < π/2 towards a wall a distance 'l' away. If 'y' is the coordinate along the wall,

show that

g(y)dy=(1/π) (1/(1 +(y/l)^{2})) (dy/l)

This is the Cauchy distribution. Assuming that the mean should be zero from symmetry considerations, try to find the standard deviation; what problem do you have? Truncate the distribution at a distance |y| = L either side of the peak. Calculate the new normalisation constant, and find the standard deviation.

Re: Cauchy distribuation and maths help

id appreciate if someone could even point me in the right direction, im abit stumped...

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Re: Cauchy distribuation and maths help

Re: Cauchy distribuation and maths help

im not sure if you read this bit...

This is the Cauchy distribution. Assuming that the mean should be zero from symmetry considerations, try to find the standard deviation; what problem do you have? Truncate the distribution at a distance |y| = L either side of the peak. Calculate the new normalisation constant, and find the standard deviation.

Re: Cauchy distribuation and maths help

Quote:

Originally Posted by

**bobby84** im not sure if you read this bit...

This is the Cauchy distribution. Assuming that the mean should be zero from symmetry considerations, try to find the standard deviation; what problem do you have? Truncate the distribution at a distance |y| = L either side of the peak. Calculate the new normalisation constant, and find the standard deviation.

Well if

Then we need to calculate the integral

So now try to calculate this integral. What do you get?

Re: Cauchy distribuation and maths help

hey i got there in the end actually,

my final solution was....

(sigma) = sqrt(4-(pie)/2(pie)) l

cheers for the help ;)