3. Suppose a value is chosen “at random" in the interval [0,6]. In other words, x is an observed value of a random variable X 4 U (0, 6). The random variable X divides the interval [0,6] into two subintervals, the lengths of which are X and 6 – X respectively. Denote by Y the length of the shorter of the two intervals. (a) Draw a picture which illustrates the value of Y as a function of the possible values of X. (b) Describe the support of Y and find the probability P(Y > y) for any given 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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