This question is an programming assignment in python

Problem 2 (Monte-Carlo Method for Integration) 15+15-30 points) In probability research, one common task is to find the expected value of a function that depends on a random variable. If the random variable is continuous, then calculating such an expected value may involve a complex integral that has no simple closed-form expression. In this scenario, one work-around is to leverage the Monte-Carlo method to find an approximate answer. (a) In this subproblem, you will be asked to tackle the following integral: Let ZN (0,1). Define another random variable y = cos(2) + sin(22). Our goal is to find out the expected value of Y using Monte Carlo method. Specifically, let 2222 ben independent numbers drawn from a standard normal distribution Then. *cos(.) + sin(2-)). ELYI = (cm() + sin(2:1) TE Homework 4. Part II: Multivariate Normal & Monte-Carlo Method Please write a short program (either in Python or MATLAB) to implement the above procedure. Suppose we sot n = 102 and repeat the same estimation procedure for 20 times. What are the estimation results? What if we reconfigure n = 10 and again repeat the same estimation procedure for 20 times. Do you observe any differences in the estimation results? (b) Define a dosed region A = {(x,y): (1-0.2)2 + 2(x +0.3)