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We consider a waiting system with a single server and finite capacity c = 3, in which the customers arrive according to a Poisson process with rate λ and the service times are independent exponential random variables with parameter μ = 2λ. When the system is full, a fair coin is tossed to determine whether the second or third customer will be the next one to be served,
(a) Write the balance equations for this system, and calculate the limiting probabilities .
(b) Calculate the average time that an arriving customer who finds (exactly) one customer in the system will spend in it.
(c) Calculate the average time that a customer who enters the system will spend in it.
If an accident occurs, the claim amount is exponentially distributed with a mean of 100. Calculate the expected value and variance of the aggregate claims over this period.
at a large university it is known that 50 of the students live on campus. the director of student life is going to take
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in the test of a certain hypothesis the p-value corresponding to the test statistic is 0.0316. can the null hypothesis
Find the probability that a random sample of size 54, selected with replacement, will yield a sample mean greater than 4.1 but less than 4.4. Assume the means to be measured to the nearest tenth.
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An engineer collected data from a random sample of water tank construction projects to build a statistical linear model that not only estimates the unit cost of water tank construction but also investigates the influence of certain factors on the..
Calculate the sample variance using the computational formula. First subtract a convenient number from each observation.
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the probability that sammy makes his own lunch is 0.75. the probability increases to 0.8 if he made his own lunch the
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