• Use statistical software R for your codes.
• Only basic built-in functions available in R are allowed.
1. For a Bernoulli process, answer the following questions
(a) Use p = 0.7 and simulate number of arrivals for t = 10,50,100,500.
(b) From part (a), plot t versus probability of number of arrivals. What do you observe.
(c) From part (a), plot t versus cumulative distribution function of number of arrivals. What do you observe.
(d) Simulate number of arrivals with p = 0.1 and t = 100 and plot the density. Describe your observations.
(e) In Bernoulli process, the interarrival times follow Geometric (p). Let p = 0.7, plot the cumulative distribution function of X1.
2. Suppose that the customers arrive at a retail store at a rate of 20 customers per minute. We are interested in studying number of customers in a long run. Let’s assume we can model it as a Poisson process. Answer the following questions
(a) Simulate the density of number of arrivals until time t = 50,100. Provide the related graphs.
(b) Simulate the cumulative distribution function of number of arrivalsuntil time t = 50,100. Provide the related graphs.
(c) In part (a) and (b), make comparison w.r.t. t.
