2. a) Let n N, and let U denote a random variable that is uniformly distributed on [0, 1]. Put Ain [(2i-1)/2", 2i/2"[ =

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2 A Let N N And Let U Denote A Random Variable That Is Uniformly Distributed On 0 1 Put Ain 2i 1 2 2i 2 1 (39.13 KiB) Viewed 45 times

2. a) Let n N, and let U denote a random variable that is uniformly distributed on [0, 1]. Put Ain [(2i-1)/2", 2i/2"[ = as well as 2n-1 Xh = Σ 1A (U), where 14 denotes the indicator function of a set A. Show that (Xn)neN is an iid sequence of random variables that are uniformly distributed on {0, 1}. b) Conversely, let (Xn)neN denote an iid sequence of random variables that are uniformly distributed on {0, 1}. Show that 00 U= ΣX₁/2" n=1 is uniformly distributed on [0, 1].