I have a word problem regarding the cdf and I am struggling to get my head round the idea. It goes like this:
A dart is thrown at a circular target with radius $\alpha$. The dart always hits the target and The probability that the dart hits any particular region of the target is proportional to the area of that region. Let $R$ be the distance between the target centre and the point the dart hits. I must find the cdf for $R$.
I know that the point of contact is uniformly distributed over the target but that is basically it. If someone can run through how I would do this, it would help greatly.