Generate a sequence of i.i.d. (independent identically distributed) random variables T = {Tn, N ≥ n ≥ 1} which are geometrically distributed with parameter (intensity) p = 0.1 for N = 5000, 10000, 50000. The random variable Tn for such case is governed by the distribution P{Tn = k} = (1 − p)^{k−1} p, k = 1, 2, 3, ⋯. To verify the results you obtain, for each case of N, please A. Draw probability distribution histograms which show the relative frequency of T in terms of n, for n = 1, 2, ⋯, 30. B. Compute the sample mean and sample variance. Compare your simulation results with the theoretical values. Note (1): The i.i.d. sequence T = {Tn, N ≥ n ≥ 1} often represents the inter arrival time sequence for the discrete time stochastic processes. In such process, time is divided into slots. Each slot is of unit length and is marked by discrete times 1, 2, ⋯,. An event (arrival) may occur with probability p within one slot duration and is recorded at the end of the slot. If the sequence T is geometrically distributed, the corresponding arrival process A is called the geometric point process. Note (2): To generate a sequence of i.i.d. Geometric random variable T = {Tn, N ≥ n ≥ 1} with the parameter p, 0 < p < 1, you may first generate a sequence of i.i.d. uniform random variables U = {Un, N ≥ n ≥ 1} over [0, 1]. Then for each sample, use the transformation Tn = 1 + [ln Un / ln(1 − p)]. where [x] represents the largest integer less than or equal to x.