We will first do some preliminary work that will enable us to simulate stochastic realisations of the prices of the stocks of interest. (a) Derive an explicit mathematical formula for the cumulative distribution function of the Laplace distribution. [2] (b) Describe a simple approach for the generation of random deviates from the Laplace distribution. [4] (c) Write a program that generates 100000 samples from the Laplace distribution with u = 0.5 and b = 0.3 (use the approach you developed in the previous question; do not use built-in functions for this). To verify that your method works correctly, show a histogram of these samples and a line-graph of the probability density function (both in the same plot). [6] We will first do some preliminary work that will enable us to simulate stochastic realisations of the prices of the stocks of interest. (a) Derive an explicit mathematical formula for the cumulative distribution function of the Laplace distribution. [2] (b) Describe a simple approach for the generation of random deviates from the Laplace distribution. [4] (c) Write a program that generates 100000 samples from the Laplace distribution with u = 0.5 and b = 0.3 (use the approach you developed in the previous question; do not use built-in functions for this). To verify that your method works correctly, show a histogram of these samples and a line-graph of the probability density function (both in the same plot). [6]