2. Simulation study Suppose that X1, . ..; Xn are independent and identically distributed (iid) binomial random variables such that P(Xi = 1 | k, P) = (x)p (1 -p)* z, x =0,1, ..., k for all i = 1, ..., n. Assume that both k and p are unknown and use the method of moments to obtain point estimators of both parameters. This somewhat unusual application of the binomial model has been used to estimate crime rates for crimes that are known to have many unreported occurrences. For such a crime, both the true reporting rate, p, and the total number of occurrences, k, are unknown. Equating the first two sample moments to those of the population yields the system of equations X = kp and Ex? = kp(1 -p) + hip, where X is the sample mean. Solving for k and pleads to k= X - (1) EL,(X; - X)2 and p = It is difficult to analyze the performance of k and p analytically so you are asked to perform a simulation study using R . The idea is to generate random samples and investigate the performance of & and p using random samples. 1. Generate a single simple random sample of length n