31 Starting with the R function for the simulation of the immegration -death process, modify it to inclube " birth's in addition to immigrations and death Use your modified function to simulate a bug realisation from the birth-immigration- death process where the birth, death, and immigration rates are all one, starting from an initial condition of zero.1:) Question 15 1 pts Which of the following are ways of controlling for confounding in the study analysis phase? (Select all that apply) [3 Matching [j Multivariate analysis D Restriction [j Stratication 1. Suppose (X, Y, Z) follow the multivariate normal distribution: 1 0.4 0.2 ( X , Y, Z ) ~ N 3 0.4 1 0.3 (2) 0.2 0.3 1 (a) Find the distribution of X + Y + Z; (b) Find Cov(2X - 3Y + Z, X + Y - Z). Hint for 1.: A linear transform of a univariate/multivariate normal r.v. is a univariate/multivariate normal random variable. A univariate/multivariate normal random variable is entirely characterized by its mean and its variance / covariance matrix