IT_Y4_new

# Define variables and event lists to analyze this

This preview shows pages 120–122. Sign up to view the full content.

Define variables and event lists to analyze this model and write the procedure for this system. (20 marks) 5. Consider a shop that stocks a particular type of product that it sells for a price of r per unit. Customers demand in accordance with a Poisson process with rate λ and the amount demanded by each one is a random variable having distribution G. In order to meet demands, the shopkeeper must keep an amount of the product on hand and if the on-hand becomes low, additional units are ordered from distributor. If present inventory level is x and no order if outstanding, then if x<s, the amount s-x is ordered. The cost of ordering y units of product is a specified function c(y) and it takes l units time until order is delivered. In addition, the shop pays an inventory holding cost of h per unit item per b unit time. Whenever customers demands more of the product than is presently available, than the amount on hand is sold and the remainder of the order is order is lost to the shop. Define variables and events to analyze this model and estimate the shop’s expected profit up to fixed time T. (10 marks) 6. Suppose that the different policyholders of a casually insurance company generate claims according to independent Poisson process with a common rate λ , and that each claim amount has distribution F. Suppose also that new customers sign up according to a Poisson process with rate v, and each existing policyholder pays the insurance

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
firm at a fixed rate C per unit time. This system states with n customer and initial capital a 0, find then. Define the variable and enters for this system and estimate the probability that the firm’s capital is always non negative at all times up to time T. (20 marks) 7. A system needs n working machines to be operational. To guard against machine breakdown, additional machines are kept available as spares. Whenever a machine breaks down it is immediately replaced by a spare and is itself sent to the repair facility, which consists of a single repair person who repair failed machines one at a time. Once a failed machine has been repaired it becomes available as a spare to be used when the need arises. All repair times are independent random variables having the common distribution function G. Each time a machine is put into use the amount of time it functions before breaking down is a random variable, independent of the past, having distribution function f. The system is said to “Crash” when a machine fails and no spares are available. Define variables and events to analyze this system and write a model in simulating to estimate the time at which the system crashes. (20 marks) 8. Draw a flow diagram for simulating the Repair model. (10-marks) 9. The quantity X = which is the arithmetic average of the n data values, is called the sample mean. Proved that X, sample mean is an unbiased estimator of population mean θ . And also find its mean square error. (10 marks) 10. The quantity S 2 = 2 1 ( ) 1 i i n X X n = is called the sample variance and show that sample
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern