modeling and simulation question The mean time between arrivals of customers in a bank is 4 minutes. If a customer has already arrived in the bank, a) What is the probability that the next arrival will come after 5 minutes, if it follows exponential distribution? b) What is the probability that 6 customers will arrive in one-hour interval, if it follows Poisson distribution? II) Assume that the inter-arrival time is Poisson process distributed with a mean of 10 per hour and the service time has the exponential distribution with one customer every 5 minutes, and the system operates 8 hours a day. Assume you have M/M/1 queuing model, find (a) The utilization of the system. (b) The expected number in the queue. (c) The average waits in the queue. (d) The average waits in the system. (e) The number in the system. (f) The average cost per day from waiting if you assume the cost is JD10 for each hour lost by a customer waiting.

TOPIC: MARKOV CHAINS An electronic device manufacturer orders 2-meter-long conductors from a supplier, who claims that the wire in its conductors has the specified mechanical strength desired by its engineers.that the wire of its conductors has the specified mechanical strength desired by the company's engineers for use in experimental models.for use in experimental models. Each shipment is rated by the technicians who use it as"satisfactory" (nothing is reported to the supplier), as "substandard" (the supplier is notified in writing that the consignment does not meet the standards), or as "substandard" (the supplier is notified in writing that the consignment does not meet the standards).(the supplier is notified in writing that the shipment does not meet specifications), or as "unacceptable" (the shipment is returned, and in accordance with thethe supplier replaces it with another one that has been 100% verified). The classification thus depends on thedegree to which the material…

Consider the following time series for a simple Moving Average Model, Yt = −2+ € + 0.5€t-1 • In the above, Et is considered white noise, i.e., normally-distributed with mean = 0 and variance = 4. a. Find the mean function of the time series. b. Find the variance of the time series. c. Find the lag=0 autocorrelation of the time series. d. Find lag-2 autocorrelation for this time series. e. Is the time series stationary?

A computer store maintains a maximal inventory of 30 fax machines (units). On average,one unit is sold per day, but some days experience a burst of customers. A marketingsurvey suggests that customer inter-arrival times are iid exponentially distributed withrate 1 per day. When inventory drops down to 5 units on-hand, an order of 20 units isplaced to the supplier, and the order arrives in 5 to 10 days, uniformly distributed.Unsatisfied customers check back with the store and wait for the order to arrive(backordering case). Keep in mind that another order is placed immediately upon orderarrival, should the inventory level fall below the reorder level after satisfying allbackorders.a. Develop an Arena model of the computer store, and simulate it for 2 years ofdaily (9:00 AM to 5:00 PM) operation. Save the model (i.e. Arena file with doeextension) Show the set up of the model flowchart and steps to create each part.Based on the Arena Model b. Estimate the following statistics:• Average…