Report the probability of the Trees state in the stationary distribution for the three-state ecosystemmodel to two digits after the decimal. There are three kinds of vegetation in an ecosystem: grass (G), shrubs (S), and trees (T) (Bodine, Lenhart, and Gross2014). Every year, 25% of grassland plots are converted to shrubs, 20% of shrub plots are converted to trees, 8% of treesare converted to shrubs, and 1% of trees are converted to grass; the other transition probabilities are 0.

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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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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.)
A company retains a psychologist to assess whether job applicants are suited for assembly‑line work. The psychologist classifies applicants as one of ?A (well suited), ?B (marginal), or ?C (not suited). The company is concerned about the group ?D , where an employee leaves the company within a year of being hired. Data on all people hired in the past five years give the probabilities shown. ?(?)=0.4P(A)=0.4 ?(?)=0.3P(B)=0.3 ?(?)=0.3P(C)=0.3 ?(? and ?)=0.1P(A and D)=0.1 ?(? and ?)=0.1P(B and D)=0.1 ?(? and ?)=0.2P(C and D)=0.2 Select the correct Venn diagram of the events ?,?,?,A,B,C, and ?D showing the probabilities of all combinations of psychological assessment and leaving (or not) within a year.
A. P (win/regular) = 0.82 P (win/prevent) = 0.64 Conclusion: You are more likely to win by playing prevent defense. B. P (win/regular) = 0.33 P (win/prevent) = 0.67 Conclusion: You are more likely to win by playing prevent defense. C. P (win/regular) = 0.82 P (win/prevent) = 0.64 Conclusion: You are more likely to win by playing regular defense. D. P (win/regular) = 0.33 P (win/prevent) = 0.67 Conclusion: You are more likely to win by playing regular defense.
Suppose an experiment has five equally likely outcomes: E1, E2, E3, E4, E5. Assign probabilities to each outcome and show that the requirements in equations (4.3) and (4.4) are satisfied. What method did you use?
The U.S. Department of Transportation reported that during November, 83.4% of Southwest Airlines' flights, 75.1% of US Airways' flights, and 70.1% of JetBlue's flights arrived on time (USA Today, January 4, 2007). Assume that this on-time performance is applicable for flights arriving at concourse A of the Rochester International Airport, and that 40% of the arrivals at concourse Aare Southwest Airlines flights, 35% are US Airways flights, and 25% are jetBlue flights. a) Deveiop a joint probability table with three rows (airlines) and two
A manufacturing company is faced with the problems of choosing four products to manufacture. The potential demand for each product may turn out to be good, satisfactory, or poor. Probabilities for each type are given below: Products Probabilities Good Satisfactory Рoor A 0.60 0.20 0.20 В 0.75 0.15 0.10 C 0.60 0.25 0.15 D 0.50 0.20 0.30 The estimated profit/loss under different states of demand may be taken as under. uct Profit or Loss Good Satisfactory Poor A 40,000 10,000 1,100 40,000 20,000 |-7,000 C 50,000 15,000 |-8,000 D 40,000 18,000 15,000 Prepare expected value table and advice the company about the choice of the product.
In a certain community, eight percent of all adults over age 50 have diabetes. If a health service in this community correctly diagnosis 95% of all persons with diabetes as having the disease and incorrectly diagnoses ten percent of all persons without diabetes as having the disease, find the probabilities that: The health service will diagnose an adult over age 50 as having diabetes. A person over 50 diagnosed by the health service as having diabetes actually has the disease.
On a certain stretch of the East Coast Expressway, on average three birds per week are killed colliding with passing vehicles. The highway authority decides that if the probability of more than three birds per week being hit is more than 0.1, a special committee will be appointed to deal with the problem. Q1 (a) Determine whether the special committee will be appointed or not.
The purchase patterns for two brands of toothpaste can be expressed as aMarkov process with the following transition probabilities: Which brand appears to have the most loyal customers? Explain.
At the beginning of each day, a patient in the hospital is classifed into one of the three conditions: good, fair or critical. At the beginning of the next day, the patient will either still be in the hospital and be in good, fair or critical condition or will be discharged in one of three conditions: improved, unimproved, or dead. The transistion probabilities for this situation are Good Fair Critical Good 0.65 0.20 0.05 Fair 0.50 0.30 0.12 Critical 0.51 0.25 0.20 Improved Unimproved Dead Good 0.06 0.03 0.01 Fair 0.03 0.02 0.03 Critical 0.01 0.01 0.02 For example a patient who begins the day in fair condition has a 12% chance of being in critical condition the next day and a 3%…
A study of young children was designed to increase their intake of whole-grain, rather than regular-grain, snacks. At the end of the study, the 79 children who participated in the study were presented with a choice between a regular-grain snack and a whole-grain alternative. The whole-grain alternative was chosen by 55 children. You want to examine the possibility that the children are equally likely to choose each type of snack. H0: p = 0.5Ha: p ≠ 0.5 Perform the significance test. (Use α = 0.01. Round your test statistic to two decimal places and your P-value to four decimal places.)
A study conducted by the Urban Energy Commission in a large metropolitan area indicates the probabilities that homeowners within the area will use certain heating fuels or solar energy during the next 10 years as the major source of heat for their homes. The following transition matrix represents the transition probabilities from one state to another. Electricity 10.2 Natural Gas Fuel Oil Solar Energy Elec. Gas Oil 0.60 0.05 0.10 0.15 0.85 0.10 0.08 Solar 0 0.10 0.02 0.75 0.08 0.15 0.08 0.05 0.84 Among homeowners within the area, 20% currently use electricity, 35% use natural gas, 40% use oil, and 5% use solar energy as the major source of heat for their homes. In the long run, percentage of homeowners within the area will be using solar energy as their major source of heating fuel? (Round your answer to one decimal place. Assume the trend continues.) X % what

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