I will substitute 200 z-values into the formula (1) to obtain a dependent variable, Y(i) for each row. Right after calculating all the dependent variables, I will use computer packages to capture the relations with mean and variance coming along. Is it correct to do as I explain?

Overview: In probability and statistics, it is important to understand the mean and variance for any random variables. In this exam, suppose that Y = V(X1, X2) is a random variable whose distribution depends on two independent variables X, and X2, and the objective is to estimate two deterministic functions of X] and X2: one is the mean a(X1, X2) = E(Y) and the other is the variance V(X1, X2) = Var(Y). Background: The motivation of the random variable Y = Y(X1, X2) is from overshoot analysis of random walks in applied probability and renewal theory. For a given pair of (X1, X2), one first generates a m-dimensional vector, (21, Z2, .". ; Zm), say, m = 50, which has a multivariate Gaussian distribution with m-dimensional mean vector and m x m covariance matrix depending on both X] and X2. Then the random variable Y = Y(X1, X2) is defined as Y = Y(X1, X2) = 100 . max(ed , e-, . !ezm) Zitextstem (1) Here we multiply by 100 since the numerical values of Y' might be too small in our context otherwise. Clearly 0