Generate 1000 samples for each of the following continuous random variables:
(a). Exponential distribution with λ = 1.2 and λ = 2.1
(b). Normal distribution with μ = 3.1, σ^{2} =5 and μ = 1, σ^{2} = 2
For each class of the above distribution, plot the cumulative distribution function for each set parameters on one figure (you should have two curves on each figure and have overall two figures). In addition, you should also plot the corresponding analytical results (CDF curve based on distribution formulas) on the same figure. In this way, you can verify whether your simulated random variables match with analytical results.
In addition, calculate the mean value and variance of generated samples for each distribution (sample mean and sample variance). Compare the results with the analytical results.