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1. Consider an in?nite server queuing system in which customers arrive in accordance with a Poisson process with rate λ, and where the service distribution is exponential with rate μ. Let X(t) denote the number of customers in the system at time t. Find
(a) E[X(t + s)|X(s) = n];
(b) Var[X(t + s)|X(s) = n].
2. Suppose that people arrive at a bus stop in accordance with a Poisson process with rate λ. The bus departs at time t. Let X denote the total amount of waiting time of all those who get on the bus at time t. We want to determine Var(X). Let N(t) denote the number of arrivals by time t.
(a) What is E[X|N(t)]?
(b) Argue that Var[X|N(t)]= N(t)t2/12.
(c) What is Var(X)?
A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years, respectively.
You want to estimate today's mean temperature, so you make a series of measurements (taken as a sample) throughout the day. The mean of these measurements is 63 degrees Fahrenheit, and their standard deviation is 3.4 degrees Fahrenheit.
Some studies suggest a beta-carotene intake over 3000 mcg may protect against ?macular degeneration. What percentage of people has a dietary beta-carotene intake of at least ?3000 mcg?
Over many years of administering tests to my statistics students I have found that the overall average of the scores on the first exam that I give each semester is 76.
Develop separate schedules by using the FCFS,SPT and EDD rules. Compare the schedules on the basis of average flow time,the average early time and average past due hours for any order.
suppose five 6 oz tubes of toothpaste are randomly selected and squeezed until no more toothpaste will come out. then
a company that produces dvd drives has a 9 defective rate. let x represent the number of defectives in a random sample
What is the seller's expected revenue in both auctions and does revenue equivalence still hold?
elementary 201 766 148 218 519 396 274secondary 50 280 27 41 108
The Genetics & IVF Institute conducted a clinical trial of the XSORT method designed to increase the probability of conceiving a boy. As of this writing, 291 babies were born to parents using XSORT method, and 239 of them were boys. Use a 0.01..
suppose that there are a total of 18 students in an elementary school class. the teacher assigns each of the students a
Find the present value given that interest rates are a constant 6%, vnnpx = 0.4 and Ax(1n) = 0.2. Assuming UDD, find a formula for the present value in terms of end-of-the-year-of-death insurances.
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