Please Use R to answer this question

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.

m₁ : mean of the first random variable.

m₂ : mean of the second random variable.

₁ : standard deviation of the first random variable.

₂ : standard deviation of the second random variable.

m_{1 100 100 100 100 100 100}

_{1 10 10 10 10 10 10}

m_{2 200 200 300 300 400 400}

_{2 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

b: 0.3 0.7 0.8 0.9 1.0 1.5