Let U∼Unif(0,1)U \sim \text{Unif}(0,1)U∼Unif(0,1) and X1,X2,⋯∼Unif(0,1)X_1,X_2,\dots \sim \text{Unif}(0,1)X1,X2,⋯∼Unif(0,1) IID. Define N=min{n∈N:Xn>U}N = \text{min}\{n \in \mathbb{N} : X_n > U\}N=min{n∈N:Xn>U}. Find E[N]\mathbb{E}[N]E[N]. Enter −1-1−1 if the answer is infinite.
