We are given a random number generator that generates a uniform random variable X over the interval [0,1]. Suppose we ﬂip a fair coin and if H occurs, we report X and if T occurs, we report 2X + 1. Let Y be the reported random variable.
(a) Derive the cdf and pdf of Y [15 points].
(b) Which one is more likely to occur: Y ∈ [0,1] or Y ∈ [1,2]? Explain your answer [10 points].
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