29. In a fictional town, there are two restaurants, which we will call A and B for ease of reference. If someone eats at restaurant A onone day, there is a 76% chance they will eat there again tomorrow. And if someone eats at restaurant B on one day, there is a 82 %chance they will eat there again tomorrow. Which one of the transition matrices below correctly represents this situation?a) ABA 0.76 0.34B 0.18 0.82b) ABA 0.76 0.24B 0.18 0.82c) A BA 0.76 0.24B 0.08 0.82d) ABMain ContentA 0.24 0.76B 0.82 0.18e) None of the above.

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Answered: 29. In a fictional town, there are two…

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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From data collected by the Association of Realtors of a certain city, the following tran- sition matrix was obtained. The matrix describes the buying pattern of home buyers who buy single-family homes (S) or condominiums (C). Current State S C S .85 .35 Next State .15 .65 Currently, 80% of the homeowners live in single-family homes, whereas 20% live in condominiums. If this trend continues, what will be the percent of homeowners in this city who will own single-family homes and condominiums 2 years from now? In the long run?
We want to train a mouse to follow a particular path in the maze (see image 1). To measure the effectiveness of the training, we want to compare the behaviour of the trained mouse to that of a mouse that runs through the maze at random.(a) Construct the matrix T describing the behaviour of the untrained mouse, where tij gives the probability of going to room i when the mouse is in room j. (Note that since the mouse moves randomly if it is in front of two doors, it has a 1/2 probability of going through each of these doors.) (b) Suppose the mouse begins its journey through the maze with a vector of probabilities P(0) = (see image 3) where pi(0) represents the probability of being in room i at the start; so of course we have p1(0)+p2(0)+p3(0)= 1). Show that the probabilities of being in room i after a change of room P(1) are given by P(1)=TP(0). Indications: proceed with a proof on the one hand and on the other hand: start by calculating the probabilities of being in parts 1,2 or 3 after…
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A car rental service in a certain town has a fleet of about 600 cars, at three locations. A car rented at one location may be returned to any of the three locations. The various fractions of cars returned to the three locations are shown in the matrix to the right. Suppose that on Monday there are 295 cars at the airport (or rented from there), 65 cars at the east side office, and 240 cars at the west side office. What will be the approximate distribution of cars on Wednesday? Cars Rented From: Airport East West 0.95 0.03 0.12 0.00 0.94 0.06 0.05 0.03 0.82 Returned To: Airport East West On Wednesday, 274 cars will be at the airport, 52 cars will be at the East location, and 274 cars will be at the West location. (Round to the nearest integer as needed.)
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