(14pts) Suppose a piece of chalk has length 1. When it drops onto the floor, it...

(14pts) Suppose a piece of chalk has length 1. When it drops onto the floor, it breaks into two pieces. Suppose the breaking point is uniformly distributed on the chalk. Let X denote the length of the shorter piece and R the ratio of the lengths of the shorter to the longer piece. Then X has uniform distribution on [0, 1 2 ]. (a) (6pts) Find the probability density function of R. (b) (8pts) Find the mean and variance of R

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orchestra answered 1 year ago

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