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The needle on a broken car speedometer is free to swing, and bounces perfectly off the pins at either end, so that if you give it a flick it is equally likely to come to rest at any angle between 0 to ##\pi##.

a)Find probability density ##\rho##(##\theta##).

b)If x is the projection of needle on the horizontal line and r is length of needle, then find probability density ##\rho##(x)

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The first one is simply:

##\rho##(##\theta##)##d\theta## = ##d\theta##/##\pi##

so, ##\rho##(##\theta##) = 1/##\pi##

I couldn't do the b part. So I looked at the solution and it says:

##\rho##(##\theta##)##d\theta## = ##\rho##(x)dx

Why? Can you please tell me the reasoning?