uppose a value x is chosen "at random" in the interval [0, 1]. In other words, x is an observed value of a standard uniform random variable X d = U (0, 1). Denote by Y the distance of X from the nearest integer.

a) Express Y as a function of X. What is the support of Y ?

(b) Find P (Y > y).

c) Find both the cdf and the pdf of Y . Can you tell the name of the distribution of Y ?

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