Consider the model we used for the Doomsday problem (March 13, Example 72): Z Continuous Uniform(0.0, 5.0) YIZ~Continuous Uniform(0.0, Z) n class, we computed the marginal density of Y by computing an integral analytically. In most cases of practical interest though, it is not possible to find a nice expression for integrals involved in marginalization. In this question, we explore the basic idea behind an alternative called Monte Carlo integration. Recall that we seek to compute: f(0.06)- Jsz(nz(0.06|z)dz Equation (1) Monte Carlo integration is based on the following fact: if X1, X2,... , Xv are id with density f(x), and N is large, then the expectation ELg(Xi)] is well approximated by the sample average. In other words: A) Monte Carlo approximation Write a choice of f(x) and g(x) suitable to approximating Equation (1) B) Verification on Doomsday problem Calculations in Blang are done automatically via Monte Carlo integration. Fill the laws block to specify the Doomsday model as introduced in class. Doomsday 1 modeL 2 random RealVar Y?: 0.06 3 random RealVar Z ?: latentReal 4 Laws // Fill this