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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Example 41 Fifty students were surveyed, and asked if they were taking a social science (SS), humanities (HM) or a natural science (NS) course the next quarter. 26 were taking a HM course 9 were taking SS and HM 10 were taking HM and NS 7 were taking none 21 were taking a SS course 19 were taking a NS course 7 were taking SS and NS 3 were taking all three How many students are only taking a SS course? It might help to look at a Venn diagram. SS a NS b g C h HM
Selecting the Appropriate Inferential Test: For each of the studies below, please identify the following (or indicate N/A "not applicable" if the feature is not relevant to the design): a) Independent Variable(s) (IVs) and # of levels for any IVs (for Correlation/Regression, identify the predictor and predicted variable rather than IV and DV) b) Dependent Variable (DV) c) Scale of Measurement for the Dependent Variable: (Nominal, Ordinal, Interval, Ratio) for Correlation/Regression please make sure you identify the scale of measurement for both variables d) Appropriate Statistical Test (If it is a Factorial ANOVA, make sure to name the design: e.g., 2 X 2, 2 X 3, etc.)
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?
4. In an animal experiment, three mice with dandruff in their hair are washed with hair shampoo. The mice are named Alpha, Bravo and Charlie. From many previous animal experiments, it is known that (i) Alpha, Bravo and Charlie have no dandruff after washing in 30%, 45% respectively 65% in most cases they no longer have dandruff. (ii) The shampoo on Alpha, Bravo or Charlie in 95% of the cases works.
1
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)?
3. In how many ways can this diagram be coloured subject to the following two conditions? (i.) Each of the smaller triangle is to be painted with one of the three colours: White, black or blue. (ii.) No two adjacent regions have the same colour. If "C,, = "C,, then n is equal to %3D 4. If "P, = 840, "C, = 35, then r = 5. "C, + "C, - l"C,- l°C, = 6.
2. Mobile phone operator TELE2 has at least 4 tariffs: Brivais(B), Savejis(S), Smart(SM), Zelts(Z). In 2019Y the proportion of clients for each tariff is: B=5%; S=50%; SM-15%; Z=30%. Possible changes from one type of tariff to another for the following year are the following: to B to S to SM to Z from B 5% 2% 1% 1% 1% from S 3% 1% from SM 5% 5% from Z 5% 4% 3% Find initial distribution, Transition matrix (stochastic matrix), stationary distribution and plot a graph for transition of one step. bain ic the following

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