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.


m1 : mean of the first random variable.

m2 : mean of the second random variable.

σ1 : standard deviation of the first random variable.

σ2 : standard deviation of the second random variable.


m1 100 100 100 100 100 100

σ1 10 10 10 10 10 10

m2 200 200 300 300 400 400

σ2 20 30 10 20 30 40