Draw the transition probability graph and construct the transition probability matrix of thefollowing problems.2. A police car is on patrol in a neighborhood known for its gang activities. During a patrol,there is a 60% chance of responding in time to the location where help is needed; elseregular patrol will continue. chance for cancellation (upon receiving a call, there is a 10%in which case normal patrol is resumed) and a 30% chance that the car is alreadyresponding to a previous call. When the police car arrives at the scene, there is a 10%chance that the instigators will have fled (in which case the car returns back to patrol) anda 40% chance that apprehension is made immediately. Else, the officers will search thearea. If apprehension occurs, there is a 60% chance of transporting the suspects to thepolice station; else they are released and the car returns to patrol.

Answered: Draw the transition probability graph…

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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5. Given the following state transition graph and emission probabilities for each state a State 1 Output Prob 0.8 b 1 C 0.5 0.1 0.1 0.3 2 a State 2 Output C 0.5 0.2 Prob 0.2 0.6 0.2 0.5 3 State 3 Output 1 C Prob 0.7 a b 0.2 0.1 What's the probability of observing "aabbc" through state transition path 1-2-2-3-3?||
There are three kinds of vegetation in an ecosystem: grass (G), shrubs (S), and trees (T) (Bodine, Lenhart, and Gross 2014). Every year, 25% of grassland plots are converted to shrubs, 20% of shrub plots are converted to trees, 8% of trees are converted to shrubs, and 1% of trees are converted to grass; the other transition probabilities are 0. Calculate the probability of a plot of land have the following succession of vegetation from year to year: GSGG, taking the first state as given. (type three digits after the decimal).
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…
You have been assigned to test the hypothesis that the average number of cars waiting in line for the drive-thru window during lunch hour differs between Chick-fil-A, Wendy's, and McDonald's. The following data show the number of cars in line during randomly selected times during the lunch hour at all three chains. Chick-fil-A(1) Wendy's(2) McDonald's(3) 7 7 6 10 8 7 11 5 6 8 3 7 9 2 9 Perform a one-way ANOVA using α = 0.05 to determine if a difference exists in the average number of cars waiting in line at the drive-thru during the lunch hour between these chains.
1. A beverage manufacturing company uses a pair of redundant pumps to transfer flavored syrups to the bottling line. Each pump has a À of 0.055 failures per year and ß of 0.05. What is the probability that both pumps will fail during a 45 day production run? a. 0.00004 b. 0.00034 c. 0.00038 d. 0.12
2. This year Karen has decided to diversify her business by growing broc- coli as well as lettuce. Karen plants lettuce with a probability of or broccoli with a probability of . By the time these plants are ready to harvest the price of lettuce increases with a probability of and decreases with a probability of 3. The price of broccoli increases with a probability of , decreases with a probability of or stays the same with a probability of . (a) Draw a probability tree for this scenario. (b) Use the probability tree to determine the probability that Karen plants broccoli and that the price of broccoli increases by the time it is ready to harvest. (c) Use the probability tree to determine the probability that the price of whatever Karen plants increases by the time it is ready to harvest. (d) Calculate Pr(Price of lettuce does not change | Karen plants lettuce). (e) Calculate Pr(Price of broccoli does not changen Karen plants broccoli).
A circuit operates as long as there is a functional path, which does not include any dysfunctional (broken) switches on its path, between 1 and 2. The probabilities that the switches A, B, and Y are not functioning or broken (Failure, F) are 12%, (22)%, and (13)%, respectively (as shown in the figure below). The switches function independently. What is the probability that the circuit operates successfully (Success, S) from 1 to 2?
A circuit operates as long as there is a functional path, which does not include any dysfunctional (broken) switches on its path, between 1 and 2. The probabilities that the switches A, B, and Y are not functioning or broken (Failure, F) are 12%, (20+I)%, and (10+H)%, respectively (as shown in the figure below). The switches function independently. What is the probability that the circuit operates successfully (Success, S) from 1 to 2? H is 3 and I is 2
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
Is there a unique way of filling in the missing probabilities in the transition diagram shown to the right? If so, complete the transition diagram and write the corresponding transition matrix. If not, explain why. 0.3 OA. Yes. The probability of transition from A to A is probability of transition from C to B is. (Type integers or decimals.) 0.4 0.5 0.7 B 0,2 0.1 Is there a unique way of filling in the missing probabilities in the transition diagram? If so, identify the missing probabilities. If not, explain why. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. the probability of transition from B to C is and the OB. No. It is possible to find the probability of transition from A to A, but the probability of transition from B to C is needed to find the probability of transition from C to B (and vice versa). OC. No. At least one of the missing probabilities is needed to find the other two. OD. No. It is possible to find the probability…
Police plan to enforce speed limits by using radar traps at four different locations within the city limits. The radar traps at each of the locations L1, L2, L3, and L4 will be operated 40%, 30%, 20%, and 30% of the time. If a person who is speeding on her way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations, what is the probability that she will receive a speeding ticket?

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