Consider a Markov Chain with three possible states S = {1,2,3}, that has the following transition matrix. [1/2 1/4 1/4] P = |1/3 [1/2 1/2 2/3 (a) Draw the state transition diagram for this chain. (b) P( X5 = 2 | X4, = 1) (c) P(X3 = 2| X2 = 2) (d) If we know P(Xo = 1) = 1/4, find P(Xo = 1,X1 = 2) (e) If we know P(X, = 1) = 1/4, find P(X, = 1,X, = 2,X2 = 3)
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Subject: Stochastic process
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- Question 2 Example: The events A and B are mutually exclusive and P(AU B) = 0.9 P(B|C) = 0.2 P(BUC) = 0.6 P(A) = P(B) + P(C) Find P(B) and P(C) and show that B and C are statistically independent.QUESTION 14 Prior to a set of compensation policy changes at a company 31% of the employees surveyed said that they liked their job very much, 48% said that they liked their job moderately, and the remaining employees said that they were dissatisfied with their job. Now, in a survey of 190 employees, 63 said they liked their job very much, 104 said that they liked their job moderately, and the remaining employees said that they were dissatisfied with their job. When testing (at the 5% level of significance) whether the proportions have changed, what is the test statistic? (please round your answer to 3 decimal places)QUESTION 15 Prior to a set of compensation policy changes at a company 31% of the employees surveyed said that they liked their job very much, 45% said that they liked their job moderately, and the remaining employees said that they were dissatisfied with their job. Now, in a survey of 202 employees, 76 said they liked their job very much, 106 said that they liked their job moderately, and the remaining employees said that they were dissatisfied with their job. When testing (at the 5% level of significance) whether the proportions have changed, what is the critical value? (please round your answer to 3 decimal places)
- Cases 1.1 Tattoos Aren't Us When teen actresses Liv Tyler and Alicia Silverstone appeared in the popular video for the Aerosmith song "Crazy," the belly rings they wore created a demand for body piercing in places other than the ear. Also, tattoos, traditionally associated with sailors and tough guys, have become popular. Today body piercing shops and tattoo parlors are other housed in the same establishment. The rise in the phenomenon of tattooing and body piercing did not escape the attention of Burton Ritchie, owner of The Psychedelic Shack, a shop that caters to the popular culture market. Burton, a marketing major in college, had developed a successful business by carefully observing trends in the market and sensing which trends would become profitable business lines. His tattooing business was based on solid facts about the market. By the early 2000s, 10 percent of Americans have or have had a tattoo. Research also showed tattooing was a youth phenomenon. Burton knew, based on…Question 1 Classify the type of random variable: Blood types collected in a donation drive O continuous O not a random variable discreteSection 3.3 Brent Perry works as a guide and conservationist for an ornithological tourism company, which is part of an emerging industry catering to birders. He recently surveyed the bird populations in some preserved deciduous woodlands in Northern New Jersey. In particular, he was looking for Baltimore Orioles who surprisingly to some have taken up residence in Jersey elms and maples. On five random visits each along five separate and independent mile-long pathways (Trails A through E), he recorded the following numbers of sightings of Baltimore Orioles: Trail A 8 16 8 12 16 Trail B 1 15 9 8 7 Trail C 22 10 16 10 22 Trail D 19 29 24 29 19 Trail E 16 24 16 24 20 He kept other variables about his bird watching as constant as he reasonably could. He wonders if all five pathways provide comparable opportunities to spot these orange-plumed birds. Help Brent with his analysis by completing the following…
- How many six-number combinations can be generated from the numbers from 1 to 42 inclusive, without repetition and with no regards to the order of the numbers?Question 5 Germination of a seed commences with the uptake of water and is completed with the appearance of the embryo, in most species radical first, through the surrounding structures. Table 1 gives data regarding germination rates for treated and untreated seeds. (a) At 1% significance level, is the germination rate the same for the treated and the untreated seed? (b) Table 1: Germination rates for treated and untreated seeds Germinated Not Germinated 15 30 85 120 (c) Treated Untreated State a suitable null and alternative hypotheses for the problem. Test the hypotheses in part (a) by using x² test. Write your conclusion.QUESTION 6 Suppose there are 115 patients in a clinical trial. Of those, 35 received a real medication and were cured of their illness, 20 received the real drug and were not cured, 28 received a sugar pill (placebo) and were not cured and the remaining received a sugar pill and were cured. When testing (at the 5% level of significance) whether the medication was effective (or thinking about it another way, testing whether getting the medication and being cured is independent or not), what is the critical value (please round your answer to 3 decimal places)