a) A study has determined that the occupation of a boy as an adult, depends uponthe occupation of his father and is given by the following transition matrix, whereP = professional, F = farmer, and L = laborerFather's occupationP FP [0.80.30.2]Son'sF0.10.50.2оссираtionL 0.10.20.6Thus the probability that son of a professional will also be a professional is 0.8 andso on.i)What is probability that the grandchild of a professional will be a farmer?ii)In the long run, what proportions of the population will be former?

Answered: Image /qna-images/answer/6f1efcbf-e054-4c9a-a80f-ed3d0627c5b0.jpg

Answered: a) A study has determined that the…

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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The following data consists of a matrix of transition probabilities (P) of three competing companies, the initial market share state ℼ(1), and the equilibrium probability states. Assume that each state represents a firm (Company 1, Company 2, and Company 3, respectively) and the transition probabilities represent changes from one month to the next. The market share of Company 3 after three periods is a. 0.259 b. 0.261 c. 0.283 d. 0.296
The management is faced with the problem of choosing one of the products for manufacturing. The probability matrix after market research for the two products was as follows: State of nature Acts Good Fair Рoor Product 'A' 0.75 0.15 0.10 Product 'B' 0.60 0.30 0.10 The profits that the management can make for different levels of market acceptability of the products are as follows : Profit (in USD) if market is Acts Good Fair Рoor Product 'A' 35,000 15,000 5,000 Product 'B' -1,000 20,000 Loss 3,000 Calculate expected value of the choice of alternative and advise the management.
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
Let us consider the population of people living in a city and its suburb and the migration within this population from the city and the suburbs to the city and the suburbs. The migration of these populations from and to each other is given by a stochastic matrix [.95 .03] P = |.05 .97 The entries in this matrix were obtained from collected data that demonstrates individuals are 95 % likely to remain in the city, 5 % likely to move from the city to the suburbs, 3 % likely to move from the suburbs to the city, and 97 % likely to remain in the suburbs. Now suppose in the year 2000 60 % or .6 percent of people live in the city and 40 % or .4 percent of people live in the suburbs. What will be the percentage of people living in the city be in the year 2001? What will be the percentage of people living in the suburbs be in 2002? Hint: Recall, for a general Markov Chain (S, ro, P) the initial vector ro is required to merely be a probability vector, that is, a vector whose entries add up to 1.…
The following data consists of a matrix of transition probabilities (P) of three competing companies, the initial market share state ℼ(1), and the equilibrium probability states. Assume that each state represents a firm (Company 1, Company 2, and Company 3, respectively) and the transition probabilities represent changes from one month to the next. The market share of Company 2 after two periods is a. 0.283 b. 0.26 c. 0.261 d. 0.47
Suppose a two state experiment has the following transition matrix: 0.2] 0.4 0.8 P = 0.6 Answer the following questions: 1. Find P(2). ... ... ... ... ... 2. If the experiment is in state 1 on the first observation, what is the probability that it will be in state 2 on the third observation? ... ... 3. If the experiment is in state 1 on the first observation, what is the probability it is in state 2 on the next two observations? ...
(a) The following diagram shows the movement of Kenyan households among three income groups: affluent, middle class, and poor, over the 11-year period 1980–1991. AFFLUENT 27.1% Sh72,000 (in 1994) 7.5% MIDDLE CLASS 8.5% Sh24,000 (in 1994) 30.4% POOR (i) Use the transitions shown in the diagram to construct a transition matrix (assuming zero probabilities for the transitions between affluent and poor). (ii) Assuming that the trend shown was to continue, what percent of households' classified as affluent in 1980 -1991, were predicted to become poor in 1993? (iii) According to the model, what percentage of all Kenyan households will be in each income bracket in the long term?
EXAMPLE 3 Computers in a shipment of 100 units contain a portable hard drive, solid-state memory, or both, according to the following table: Portable Hard Drive Solid-state memory Yes No Yes 15 80 No 4 1 Two computers are selected randomly, with replacement, from the the shipment. What is the probability mass function of the number of computers in the sample having both Portable Hard Drive and Solid-state memory?
Let S = {E1, E2, E3} be the sample space of an experiment and let A = {E1}, B = {E2}, and C = events from S. The probabilities of the sample points are assigned as follows: P(E,) = 0.35, P(E2) = 0.30, and P(E3) = 0.35. Find P(BC). {E2, E3} be Select one: O a. 0.65 O b. 0.70 O c. 0.35 O d. 0.30
What is the probability that those units in states 3 and 4 end up in each of the absorbing states?
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…
In this question you will find the steady-state probability distribution for the regular transistion matrix below with 3 states A, B, and C. A В с 0.4 0.4 0.2 A В 0.5 0.0 0.5 0.1 0.8 0.1 Give the following answers as fractions OR as decimals correct to at least 5 decimal places. What is the long term probability of being in state A? What is the long term probability of being in state B? What is the long term probability of being in state C?

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