3. [Simulations of Mixed Binomial Merton Model] Set up The goal is to check the quality of LPA approximations for the Mixed Binomial Merton (Vasicek) model. The algorithm is described below. We consider the following inputs: . For all cases, the individual default probability for all obligators p = E(p(Z) ) is fixed, p = 0.05.. The number of obligators m = 100 and m = 1000 . The parameter p in the Vasicek model takes values p = 0.1 and p = 0.5. . The argument r takes values x = 0.05, 0.15, 0.25...0.85] Questions . For each combination of m and p (4 combinations) and for each r calculate the probability that Fsim (x) = P(Lm 0. The beta function B(a, b) is defined as B(a, b) := ta-1 (1 - t) 6-1dt If a, b are integers, we can use factorials to compute B(a, b) (a - 1)!(b - 1)! (atb - 1)! The mean and variance of the distribution are a ab E[X] a+ b' Var [X] = (a + b )2 (a + b+ 1 )