Suppose 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 = 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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