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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 1/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 1/ μ.
(a) Use the results on regenerative processes to calculate the probability that the machine will be in working state at a (large enough) given time instant.
(b) What is the average age of the machine at time t? That is, what is the average time elapsed at time t since the most recent failure has been repaired? Assume that λ = μ.
a social worker is interested in estimating the average length of time spent outside of prison for first offenders who
In what areas of your business is it important to draw inference? Describe a time when drawing an inference may have hurt your business.
A general contractor is considering purchasing lumber from one of two different suppliers. A random sample of 12 "2x4's" of a certain length of each board is measured.
The insurance company charges an annual rate of $250 for the collision coverage. What is the expected value of the collision policy holder?
What is the mean of the sampling distribution of the (sample proportion) and what is the standard deviation of the and describe the sampling distribution of p
Now that you are familiar with the basic concepts of statistics, what are some examples of when you have seen or heard statistics used inappropriately?
Consider a charity organizations that receives random donations. Assume the donations to arrive following a Poisson process with a rate of one donation per hour in average. What is the probability that it will not be able to make the payment?
Maxwell Manufacturing makes two models of felt tip marking pens. There are 3 processing steps required for the pen production. Times (hours) are given in the table below.
Technically, "statistic" refers to which?A sample characteristic A measure of variability
(I) What does the slope of this line say about the relationship between price and number of carats? (II) What is the predicted price when number of carats =0? How would you interpret this price?
an experiment was performed to investigate the keyboard feel on a computer crisp or mushy and the size of the keys
(a) At the 98% con?dence level, test whether annual income and the amount of life insurance policies are independent. (b) Find the attained signi?cance level. (c) State any assumptions you have made in solving the problem.
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