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Consider a system with two components. We observe the state of the system every hour. A given component operating at time n has probability p of failing before the next observation at time n + 1. A component that was in a failed condition at time n has a probability r of being repaired by time n + 1, independent of how long the component has been in a failed state. The component failures and repairs are mutually independent events. Let Xn be the number of components in operation at time n. The process {Xn, n = 0, 1, . . .} is a discrete time homogeneous Markov chain with state space I = 0, 1, 2.
a) Determine its transition probability matrix, and draw the state diagram.
b) Obtain the steady state probability vector, if it exists.
a. Find the mean value of x (the mean number of systems sold). b. Find the variance and standard deviation of x. How would you interpret these values? c. What is the probability that the number of systems sold is within 1 standard deviation of its me..
For machine gun ammunition to be acceptable, the US Army requires that 96 percent of rounds fired hit a specified target. The test is to fire a 50 round burst at the target and observe whether this condition is met.
Write a statement that correctly interprets the confidence interval found in question 5. Find the critical value corresponding to a sample size of 19 and a confidence level of 99%. Find the critical value corresponding to a sample size of 19 and a ..
Lenght Of Pregnancy. A woman wrote to Dear Abby and claimed that she gave birth 309 days after a visit from her hushand , who was in the Navy. Lengths of pegnancies have a mean of 268 days and a standard deviation of 15 days. Find the z score for 308..
A Company produces candy on a production line. When operating properly, the production process will produce an average of u=140 pounds of candy per hour with a standard deviation of o=20 pounds of candy per hour.
Given this eort, why would we want to unify the Bayesian and frequentist approaches? Why should we be interested in the prior that most frequently yields exact frequentist inference.
It was reported that approximately 45% of all university professors are extroverted. Suppose you have classes with 6 different professors.
Questions based on binomial distribution, variance of the binomial distribution, discrete random variable and continuous random variables.
Determine whether the following situations represent a right, left or two-tailed test: In 1997, 43% of Americans 18 years or older participated in some form of charity work.
The supermarket is open 16 hours per day. What is the probability that the total number of customers who enter the supermarket in one day is greater than 10,000?
the file contains the total cost for four tickets two beers four soft drinks four hot dogs two game programs two
Show that X\Y has the same cardinality as X, assuming that N has smaller cardinality than X \Y (which cannot be proved in general without the axiom of choice, to be treated in §1.5). Hint: Let B be a countably infinite subset of X \Y . Then B and ..
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