5. South Bend weather, as follows:(1) If the last two days have been sunny, then 95% of the time, tomorrow will be sunny.(2) If yesterday was rainy and today is sunny, then 80% of the time, tomorrow will be sunny.(3) If yesterday was sunny and today is rainy, then 60% of the time, tomorrow will be rainy.(4) If the last two days have been rainy, then 75% of the time, tomorrow will be rainy.Using this information,(a) Model South Bend's weather as a Markov chain by giving a transition probability matrix.(b) Draw the state transition diagram for this Markov chain.(c) If tomorrow's weather depends on the last three days of South Bend weather, how many states will beneeded to model the weather as a Markov chain? And what are the possible states?

Given, PXt=Sunny|Xt-1=Sunny, Xt-2=Sunny=0.95 PXt=Sunny|Xt-1=Sunny, Xt-2=Rainy=0.80…

Answered: 5. South Bend weather, as follows: (1)…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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6. Suppose in small town there are three places to eat, one Chinese restaurant, one Mexican restaurant, and a pizza place. Everyone in town eats dinner in one of these places or has dinner at home. Assume that 20% of those who eat in Chinese restaurant go to Mexican, 20% eat at home, and 30% go to pizza place next time. From those who eat in Mexican restaurant, 10% go to pizza place, 25% go to Chinese restaurant, and 25% eats at home next time. From those who eat at pizza place 30% eat at home, 30% eat at Chinese and 10% eat at Mexican restaurant next time. Those who eat at home 20% go to Chinese, 25% go to Mexican place, and 30% to pizza place next time. (a) Construct the (one-step) transition matrix? (b) Does this Markov chain have steady-state?
2 30 Each family in Green Country is classified as living in an urban, rural, or suburban location. During a given year, 15% of all urban families move to a suburban location, and 5% move to a rural location; also, 6% of all suburban families move to an urban location, and 4% move to a rural location; finally, 4% of all rural families move to an urban location, and 6% move to a suburban location. a. If a family now lives in an urban location, what is the probability that it will live in an urban area two years from now? A suburban area? A rural area? b. Suppose that at present, 40% of all families live in an urban area, 35% live in a suburban area, and 25% live in a rural area. Two years from now, what percentage of Green Country families will live in an urban area? c. What is the future population distribution of the Green Country at the steady state?
1. Pretend that in a certain city the number of new cases of COVID was reported to be 200 new cases on Sunday. Let’s pretend that the number of new cases grows by 22% on Monday, and then after that falls by 22% on Tuesday Question C: What percent would the percent increase have to be on Monday to have a total change of zero% from Sunday to Tuesday? i.e. new covid cases go up by ???% on Monday and then down 22% on Tuesday for a total change of 0%. (Use decimals in answer if needed)
7.) Several years ago, the US began running out of telephone numbers. Telephone companies introduced new area codes and numbers were used up, and eventually almost all area codes were used up. (a) Until recently, all area codes had a 0 or 1 as the middle digit, and the first digit could not be 0 or 1. How many such area codes are possible? (b) The actual number of area codes under this system was 152. What could be the cause of the discrepancy between this number and your answer to part (a)?
1. In AP Econ, the total points accrued thus far is 800. The instructor has announced that there will be a total of 1000 points at the end of the semester. The final exam, therefore, is worth 200 points. Christina L currently has an average score of 87%. Is it possible for Christina L to squeak by with an A- in the class? Explain. Show your work. Assume an 89.5% in the class is considered an A-.
Illustration 16.60. A bank has a test designed to establish the credit rating of a loan applicant. If the persons, who default (D), 90% fail the test (F). Of the persons, who will repay the bank (ND), 5% fail the test. Furthermore, it is given that 4% of the population is not worthy of credit ; i.e., P(D) = .04. Given that someone failed the test, what is the probability that he actually will default (when given a load)? CS Scanned with CamScanner

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