1. Answer the following two questions. a) According to probability theory, if two random variables each follow a Normal distribution with given means and variances, their sum is also normally distributed with a mean equal to the sum of the means of two random variables and variance equal to the variances of the two random variables. Develop a simulation model and use the model to illustrate that this theory holds for any mean and variance. Use the following mean and variance parameters to set up your simulation model. Mi: mean of the first random variable. Ly: mean of the second random variable. 01: standard deviation of the first random variable. 02: standard deviation of the second random variable. 100 100 10 10 100 10 10 10 10 10 10 10 LLE 200 200 30 30 400 40 0 20 30 10 20 30 40 b) According to probability theory, if two random variables each follow an Exponential distribution with rates a and b, respectively, then their minimum is also an Exponential random variable with rate a+b. Develop a simulation model and use the model to illustrate that this theory holds for any rates a and b. Use the following a and b values to set up your simulation model. Note that Exponential distribution has a single parameter, which is given as "mean" in the lecture notes. Using "rate" is another parameterization method and rate is reciprocal of the "mean." a 0.1 0.2 0.3 0.4 0.5 0.6 Page | 1 b 0.3 0.7 0.8 0.9 1.0 1.5