Question: Problem 2 Modelling a continuous random variable A circular dart board has radius R. We take an arrow and aim it towards the dart board.

Problem 2 Modelling a continuous random variable

A circular dart board has radius R. We take an arrow and aim it towards the dart board. Let

X denote the distance of the point where the arrow strikes the board from its center.

(i) Find the CDF and PDF of X.

(ii) What is the probability that the arrow strikes the board in an annulus having inner radius

a and outer radius b , such that a < b < R?

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