ThemanageratCaf eJavawantstobuildasimulationmodeltoimproveoperations.The first step is to simulate customer arrivals.A baseline model assumes customers arrive with aninter-arrivaltimeZ(timebetweencustomers)thatfollowsanExponentialdistribution with rate parameter?= 2 customers per minute with PDF and CDF equations: f(z) =?e-?zF(z) = 1-e-?z (a)2 ptsUsing the inverse transform method, develop a continuous process generator for Zand generaten= 1000 samples of inter-arrival periodsz1,z2,...,z1000. List the first 10 samplesz1,...,z10and plot a histogram of all 1000zisamples. (b)1 ptComputethearrivaltimesforeachofthe1000customerst1,t2,...,t1000.The arrival time is the cumulative sum of inter-arrival times for all prior customers: t1=z1,t2=z1+z2,...,tn= n? i=1 zi=tn-1+zn List the first 10 samplest1,...,t10. (c)2 ptsCountthenumberofcustomersarrivingineach1-minuteintervalforthefirst 300minutesk1,k2,...,k300.Forexample,k1countsthenumberofcustomerswith 0.0=tiList the first 5 samplesk1,...,k5and plot a histogram of all 300kisamples. (d)1 ptTherandomvariableKjrepresentsthenumberofcustomersarrivinginthe jthminute.WhatprobabilitydistributiondoesKjfollow?(hint:whichdistribution counts the frequency of exponentially-distributed events in unit time intervals?)