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1. Consider the Markov chain with transition matrix
1/2 1/2 P = 1/4 3/4.
Find the fundamental matrix Z for this chain. Compute the mean first passage matrix using Z.
2. A study of the strengths of Ivy League football teams shows that if a school has a strong team one year it is equally likely to have a strong team or average team next year; if it has an average team, half the time it is average next year, and if it changes it is just as likely to become strong as weak; if it is weak it has 2/3 probability of remaining so and 1/3 of becoming average.
(a) A school has a strong team. On the average, how long will it be before it has another strong team?
(b) A school has a weak team; how long (on the average) must the alumni wait for a strong team?
Do you think they can be solved explicitly? Take the derivative of the gamma distribution and set it equal to zero and solve for alpha and beta to find the mle?
ten trials are conducted in a bernoulli process in which the probability of success in a given trial is 0.3. if x
A cereal manufacturer wants to determine if the filling machine is operating to specifications. The machine is specified to fill to a 12oz level.
To be from the same population? You may assume the that follows a normal distribution. values are: 2.13 1.31 1.91 1.92 1.77 1.64 2.29 1.99 2.33 2.49 2.22
as a counselor in the field of addiction you are interested in researching if online gambling is becoming more
A study of 200 apples trees showed that the average number of apples per tree was 1000. The standard deviation of the population is 200. Which of the following is the 98% confidence interval for the mean number for all apples.
Prostate cancer are actually proven correct through subsequent biopsy. JBGHI demands a sample large enough to ensure an error of ± 2% with 90% confidence. What is the necessary sample size?
Using the emperical rule solve the following problems for a distribution with a mean of 20 and a stardard diviation of 5. At least what percentage of the values will fall between 15 and 25.
1. investigating a particular stock you estimate the following returns and their associated probabilitiesprobability
Fifteen weeks later we learn that Jasmine did, indeed, pass the course. What is the probability that she was enrolled in Professor Normal"s section?
in a production process a product goes through one of the assembly lines a b or c and then goes through one of the
Finding the right job List three specific features a company or employer would need to have to make you interested in working for it.
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