Programming Assignment: Normal Deviates

a) Write a computer program that implements the Fibonacci generator Ui :=Ui−17 − Ui−5 Ui :=Ui + 1 in case Ui < 0 in the form of Algorithm 2.7. Tests: Visual inspection of 10000 points in the unit square.

b) Write a computer program that implements Marsaglia’s Polar Algorithm (Algorithm 2.13). Use the uniform deviates from a). Tests: 1.) For a sample of 5000 points calculate estimates of mean and variance.

2.) For the discretized SDE Δx = 0.1Δt + Z √ Δt, Z ∼ N (0, 1) calculate some trajectories for 0 ≤ t ≤ 1, Δt = 0.01, x0 = 0.