The normal distribution is one of the most important distribution in statistics because the nature provides numerous examples of populations of measurements that, at least approximately, follow a normal distribution (a) Use the rejection sampling method to generate a random sample of size 1000 from the standard normal distribution. Use a standard Cauchy distribution as a proposal distribution g(y). You can generate a random sample from the standard Cauchy distribution using rcauchy). Moreover, you can calculate normal density and Cauchy density using dnorm) and dcauchy) respectively. Choose c such that f(u) 3 cg() and report your choice of c. (b) Compute the sample percentiles and compare with the standard normal distribution percentiles.