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A point is chosen at random from a disc of radius 1. We use the uniform distribution on the disc meaning that the probability of a subset of the disc is equal to the area of the subset divided by π, the area of the disc. Let R be the distance from the point to the center of the disc. So R is a continuous random variable with range [0, 1]. Find the pdf of R.

So far I have that F(r)= r^2 (the cdf), so therefore f(r)=2r from [0,1]...is this the pdf for R?

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Hint: Answer check- Does your pdf integrate to $1$?

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