A rainy year is 80% likely to be followed by a rainy year and a drought is 60% likely to be followed by another drought year. Suppose the rainfall condition is known for the initial year to be ‘rainy’. Then the vector ? 0 = 10 gives probabilities of rainy and drought for known initial year

A rainy year is 80% likely to be followed by a rainy year and a drought is 60% likely to be followed by another drought year. Suppose the rainfall condition is known for the initial year to be ‘rainy’. Then the vector ? 0 = 10 gives probabilities of rainy and drought for known initial year

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Description: A rainy year is 80% likely to be followed by a rainy year and a drought is 60% likely to be followed by another drought year. Suppose the rainfall condition is known for the initial year to be ‘rainy’. Then the vector ? 0 = 10 gives probabilities of

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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I need assistence with part D
A certain system can experience three different types of defects. Let A; (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that P(41) = 0.38, P(A2) = 0.38, P(A3) = 0.42, P(A1 U.A2) = 0.65, P(41 U A3) = 0.69, P(A, U A3) = 0.72, P(41 N A2 N A3) = 0.01 (a) Find the probability that the system has exactly 2 of the 3 types of defects. (b) Find the probability that the system has a type 1 defect given that it does not have a type 2 or type 3 defect.
A certain system can experience three different types of defects. Let A, (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A,) = 0.15 P(A, U A2) = 0.17 P(A, U A3) = 0.15 P(A,) = 0.10 P(A,) = 0.08 P(A, U A) = 0.18 P(A, N Az nAz) = 0.02 (a) What is the probability that the system does not have a type 1 defect? (b) What is the probability that the system has both type 1 and type 2 defects? (c) What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect? (d) What is the probability that the system has at most two of these defects?
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Miami Beach Medical Clinic (MBMC) has about 17.5 patients arriving per hour on average. MBMC serves about 20 patients per hour on average. Also, MBMC does NOT follow the traditional M/M/1 model. A patient arriving at this facility is expected to have one of the following wait times of (0 or 1 or 4 or 6 or 8 minutes) in the queue before being served. The probabilities associated with these wait times in the queue are 0.3, 0.2, 0.3, 0.1, and 0.1 respectively. The patient’s average wait time in queue is expected to be: a. 2.3 minutes b. 7.2 minutes c. 5.6 minutes d. 3.9 minutes e. 2.8 minutes
Please help with both parts, thank you so much in advanced !
For a parallel structure of identical components, the system can succeed if at least one of the components succeeds, Assume that components fail independently of each other and that each component has a 0.08 probability of failure. Complete parts (a) through (c) below. (a) Would it be unusual to observe one component fail? Two components? It V be unusual to observe one component fail, since the probability that one component fails,, is V than 0.05. It V be unusual to observe two components fail, since the probability that two components fail,. is v than 0.05. (Type integers or decimals. Do not round.) (b) What is the probability that a parallel structure with 2 identical components will succeed? (Round to four decimal places as needed.) (c) How many components would be needed in the structure so that the probability the system will succeed is greater than 0.9998? (Type a whole number.) P Type here to search lyp
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.…
what does the equation, d/dt Π = MΠ calculate for where Π is population vector describing the overall state probability distributions and M is a 4x4 transition rate matrix?
(b) A system contains two components, A and B. The system will function so long as either A or B functions. The probability that A functions is 0.95, the probability that B functions is 0.90, and the probability that at least one is functioning is 0.97. (i)What is the probability that A functioning but B not? (ii) Component A is not but B function or B is not but A functioning
(8) Every year, each employee at a large company must select one of two healthcare plans. It is expected that 15% of the employees currently using plan A will switch to plan B and that 25% of the employees currently using plan B will switch to plan A. Out of the company's 1000 employees, 450 are currently enrolled in plan A. (a) Use a stochastic matrix to predict how many employees will be enrolled in each plan next year. (b) Use a stochastic matrix to predict how many employees will be enrolled in each plan in five years.
A factory worker will quit with probability 1/2 during her first month, with probability 1/4 during her second month and with probability 1/8 after that. Whenever someone quits, their replacement will start at the beginning of the next month. Model the status of each position as a Markov chain with 3 states. Identify the states and transition matrix. Write down the system of equations determining the long-run proportions. Suppose there are 900 workers in the factory. Find the average number of the workers who have been there for more than 2 months.