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,
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.