Simulating a Poisson process: A homogeneous Poisson process with rate can be simulated by assuming that an event occurs with probability t in a very short time interval t. Let us discretize the time in small intervals t. We will simulate this process for a total time of Nt, where N is the number of steps. Now for every step we have an event with probability t. (a) Write a Python code to simulate this process with =0.3,N=1000, and t=1102 (total time t=10 ). Check if the numerical solution of the probability distribution follows a Poisson distribution. To do this, you will have to run your code for many times and note the value of total number of events occurring every instance of the process. Plot the distribution of the number of events you get to verify it. (b) Run the program for N=10000 for only one instance and record the time interval between successive events. Show that the distribution of time interval between successive events, , is exponential given by e [Try to fit an exponential to the resulting distribution] Simulating a Poisson process: A homogeneous Poisson process with rate can be simulated by assuming that an event occurs with probability t in a very short time interval t. Let us discretize the time in small intervals t. We will simulate this process for a total time of Nt, where N is the number of steps. Now for every step we have an event with probability t. (a) Write a Python code to simulate this process with =0.3,N=1000, and t=1102 (total time t=10 ). Check if the numerical solution of the probability distribution follows a Poisson distribution. To do this, you will have to run your code for many times and note the value of total number of events occurring every instance of the process. Plot the distribution of the number of events you get to verify it. (b) Run the program for N=10000 for only one instance and record the time interval between successive events. Show that the distribution of time interval between successive events, , is exponential given by e [Try to fit an exponential to the resulting distribution]