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The lifetime of a certain machine is a random variable having an exponential distribution with parameter λ. When the machine breaks down, there is a probability equal to p (respectively, 1 - p) that the failure is of type I (resp., II). In the case of a type I failure, the machine is out of use for an exponential time, with mean equal to l/μ time unit(s). To repair a type II failure, two independent operations must be performed. Each operation takes an exponential time with mean equal to l/μ.
(a) Define a state space such that the process {X(t),t ≥ 0}, where X{t) denotes the state of the system at time t, is a continuous-time Markov chain.
(b) Calculate, assuming the existence of the limiting probabilities, the probability that the machine will be functioning at a (large enough) given time instant.
the number of books checked out at a public library by a sample of eight primary school children were recorded6 4 5 7 5
7% chance of making $40,000; a 20% chance of making $10,000; and 70% chance of making $0. How much should you be willing to pay for this deal?
Toledo, OH has been experiencing improved economic growth following huge capital investments from companies like Chrysler. You have just been hired by RGP, an agency for facilitating business expansion and location in the Toledo metropolitan area.
On average, a National Express coach arrives every two hours. What is the probability that only one bus will arrive in a four hour period?
suppose a committee of 3 people is to be selected randomly from a group consisting of 4 men and 5 women. what is the
Would the resulting sets of data represent dependent or independent samples? Why? What could the students change in the project to have it represent the other?
Federal health officials estimate that 67% of all those over age 65 receive the flu vaccine. Suppose 8 people over 65 will be randomly selected. Which of the following is the expected number that will be vaccinated in such a random sample of 8 peo..
question to play a lottery game a player must choose 6 numbers between 1 and 49. the order is not important. six
Assume that the profit from each sale is $750 for the situation in additional problem #1. What is the expected weekly profit for a salesperson?
A market researcher wants to find the 99% Confidence Interval for the average number of hours people spend online each day.
What is the probability that a customer does at least one of these two things?
What model might you suggest to model the number of purchases per minute? What is the probability that in any one minute at least one purchase is made? What is the probability that no one makes a purchase in the next 2 minutes?
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