Problem 2 (5 Points) 1. Simulate a compound Poisson process Cosesso (see Lecture 4) with parameter 1 = 1/2 on the time interval [0, 30) where the jumps Y , Y.,... are given as random variables (i = 1, 2, ...) with Z1, Z2,... Il.d. normally distributed random variables with mean 0 and variance 1 (also independent of the underlying Poisson process (N. Dosts3o). Plot a trajectory of your simulated process. Hint: Use your method from Problem 1 to simulate the underlying Poisson Process (N.)osis:0 driving the compound Poisson process (C)os1530 In ): # WRITE YOUR OWN CODE HERE I FEEL FREE TO INSERT MORE CELLS! ADD COMMENTS TO YOUR CODE ! 2. Simulate M = 10000 times the compound Poisson process from part 1 and compute the empricial mean and variance of your samples for the random variable C30. Compare your empricial values with the exact theoretical values which are given by E[C3o) = E[N30] . E[Y] and Var(Co) = E( N30] - ELY?). Hint: Recall that Ele) = 205 and E[(e)2) = ? In : + WRITE YOUR OWN CODE HERE! FEEL FREE TO INSERT MORE CELLS! # ADD COMMENTS TO YOUR CODE! Problem 2 (5 Points) 1. Simulate a compound Poisson process Cosesso (see Lecture 4) with parameter 1 = 1/2 on the time interval [0, 30) where the jumps Y , Y.,... are given as random variables (i = 1, 2, ...) with Z1, Z2,... Il.d. normally distributed random variables with mean 0 and variance 1 (also independent of the underlying Poisson process (N. Dosts3o). Plot a trajectory of your simulated process. Hint: Use your method from Problem 1 to simulate the underlying Poisson Process (N.)osis:0 driving the compound Poisson process (C)os1530 In ): # WRITE YOUR OWN CODE HERE I FEEL FREE TO INSERT MORE CELLS! ADD COMMENTS TO YOUR CODE ! 2. Simulate M = 10000 times the compound Poisson process from part 1 and compute the empricial mean and variance of your samples for the random variable C30. Compare your empricial values with the exact theoretical values which are given by E[C3o) = E[N30] . E[Y] and Var(Co) = E( N30] - ELY?). Hint: Recall that Ele) = 205 and E[(e)2) = ? In : + WRITE YOUR OWN CODE HERE! FEEL FREE TO INSERT MORE CELLS! # ADD COMMENTS TO YOUR CODE