Suppose the rate of accident on a highway in Texas is 2 accident

per day. We are interested in studying number of accidents in a long run.

Let's assume that the number of accidents happening till time t follows

Poisson distribution. Further assume the process started on June 1, 2020.

Answer the following questions

(a) Assuming that each interval is 1 day long, simulate and plot the

distribution of number of failures from June 1, 2020 to June 30,

2020.

(b) Simulate the density and cumulative distribution function of number

of arrivals until time t. Provide the related graphs.

(c) Let's assume there is a highway in Colorado. The rate of accident of

the highway is 5 accidents per day. Further assume that the accidents

happening at the highway is independent of those occurring on Texas

highway. Answer the following

i. Compare the number of accidents of both the processes.

ii. Explain how can we study the processes as a combined process.

iii. Simulate and plot the density of the total number of accidents

in a month (say June 1 to June 30, 2020).