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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Answered: There are three kinds of vegetation in…

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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1. A gadget has three temperature options (Low, Medium, and High) and two power settings (On and Off). You conduct an experiment where you observe the status of the machine throughout its day-to-day use, and the probabilities associated with each of the possible outcome pairs is shown. Consider the following events:A: {On}B: {Medium or On}C: {Off and Low}D: {High}Find P(B) A. .65 B. .5 C. .6 D. .72 LOW MEDIUM HIGH ON .5 .1 .05 OFF .25 .07 .03
.A system is composed of 6 subsystems A, B, C , D, E, F as indicated in fig.1. If all of them function independently with probabilities P(A)=.9, P(B) =8, P(C) = .7 P(D) = P(E) = .5, and P(F) what is probability of successful system operation? P(F) = .5 B C .8 .9 .7 .5 .5 .5
If P(A) = 0.52, P(B) = 0.45 and P(A u B) = 0.76, then P(B | A) = (Enter a number between 0 and 1, using two decimal points)
Suppose you are a broker (of junk bonds) who buys only bonds that have a 55% chance of not defaulting. You want to put together a portfolio of bonds with at least four that will not default. You want to be 93.9% sure that at least four will not default. How many bonds should you buy?
The following equally likely outcomes have been estimated for the returns on Portfolio G and Portfolio H: Scenario Portfolio G Portfolio H 1 5.0% 9.0% 2 3.0% -7.0% 3 9.0% 15.0% 4 9.0% -4.0% Which of the two portfolios is riskier? a. Portfolio H since it has the possibility of a negative return b. Portfolio G since it has the higher expected return c. Both portfolios are equally risky since the possible returns of each are equally likely to occur d. Portfolio H since its returns are more widely dispersed around the expected…
Suppose a distribution center is considering three options for expansion. The first one is to expand into a new plant, the second to add on third-shift to the daily schedule, and third, a small expansion to the existing facility. There are three possibilities for demand. These are high, medium, and low having probabilities of 40%, 33%, and 27% respectively. Suppose that the profits for the expansion plans are as follows: The new plant expected outcomes are $110,000, $50,000, -$15,000, the third shift consideration would result in outcomes of $40,000, $20,000, $-5,000 and the small expansion choice would in the following dollar amounts $15,000, $13,000, -$1,500. The amount that the company must invest in each alternative is: new plant = $48,000, third shift = $15,100, small expansion = $8,700 a. The profit/loss (EMV) for the new plant is $ [Select] b. The profit/loss (EMV) for adding a third shift is $ [Select] c. The profit/loss (EMV) for the small expansion is $ [Select] d. Which of…
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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.
Refer to the contingency table shown below. Smoking by Race for Males Aged 18 to 24 Smoker(S) Nonsmoker(N) Row Total White(W) 290 560 850 Black(B) 30 120 150 Column Total 320 680 1,000 Click here for the Excel Data File (a) Calculate the probabilities given below (Round your answers to 4 decimal places.): Smoking by Race for Males Age 18-24 Smoker Nonsmoker Row Total (S) (N) White (W) 290 560 850 Black (B) 30 120 150 Column Total 320 680 1000 Smoking by Race for Males Age 18-24 Smoker Nonsmoker Row Total (S) (N) White (W) 290 560 850 Black (B) 30 120 150 Column Total 320 680 1000
A system has six components connected as shown in the following diagram: A Assume A, B, C, D, E, and F function independently. If the probabilities that A, B, C, D, E, and F fail are 0.01, 0.05, 0.02, 0.08, 0.10, and 0.05 respectively, what is the probability that the system fails?
blindness. Would these results be surprising? Explain why or why not. 4) At the end of basketball practice, each player on the team must shoot free throws until he makes 10 of them. Slim is a 70% free-throw shooter. That is, his probability of making any free throw is 0.70. Given this information, the dotplot below shows a simulation of 120 trials of shooting 12 free throws with a 0.70 chance of making any free throw. : 4 : 5 6 8 9 7 Number of Made Free Throws 10 11 red-green color 12 a) Explain what the two dots at 5 represents. b) Use the simulation to estimate the probability that Slim makes 10 or more free throws. 3 1297091 c) Based on the results from the simulation, how many free throws is Slim most likely to make in 12 attempts? d) Therefore, based on your answer to part (c), how many total attempted free throws do you predict Slim will have to take before he can finish practice and go home.
Students in a class like to secretly use online calculators in their quizzes. There are three such online calculators favoured amongst the students: WolframAlpha (WA), Symbolab (S), and GeoGebra (GG). A student's favourite calculator changes from quiz to quiz according to the following rules: If a student likes WA best, then it is has a 50% chance of remaining their favourite for the next quiz; 25% of becoming S for the next quiz; and 25% of becoming GG for the next quiz. If a student likes S best, then it has a 50% chance of becoming WA for the next quiz, and a 50% chance of becoming GG for the next quiz. If a student likes GG best, then it has a 33.3% chance of becoming any of the three calculators for the next quiz. For the first quiz, there are 120 who count WA as their favourite; 80 who count S as their favourite; and 50 who count GG as their favourite. What is true about the fourth quiz? Choose one of the following: 1. 115 students favour WA; 52 students favour S; and 83…

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