{1,2, 3, 4}, that is, a random walk with transitionConsider an unbiased random walk on the set Sprobability p = - What is the probability of moving from state 3 to state 1 in exactly two steps if therandom walk has reflecting boundaries?

Consider an unbiased random walk on the set S = {1,2,3, 4}, that is, a random walk with transition probability p = random walk has reflecting boundaries? 1 What is the probability of moving from state 3 to state 1 in exactly two steps if the

Consider an unbiased random walk on the set S = {1,2,3, 4}, that is, a random walk with transition probability p = random walk has reflecting boundaries? 1 What is the probability of moving from state 3 to state 1 in exactly two steps if 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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1. A machine can be in one of four states: 'running smoothly' (state 1), 'running but needs adjustment' (state 2), 'temporarily broken' (state 3), and 'destroyed' (state 4). Each morning the state of the machine is recorded. Suppose that the state of the machine tomorrow morning depends only on the state of the machine this morning subject to the following rules. • If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. • If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine…
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you are given the following set P of 9 sets p= (1,1), (1,2),(1,3),(2,1),(2,2),(3,1),(3,2),(3,3).if two different points are randomly selected, what is the probability that the midpoint of these two selected points will also belong to set P??
9. A service station has one gasoline pump. Cars wanting gasoline arrive according to a Poisson process at a mean rate of 15 per hour. However, if the pump already is being used, these potential customers may balk (drive on to another service station). In particular, if there are n cars already at the service station, the probability that an n arriving potential customer will balk is for n = 1, 2, 3. The time required to service a car has an exponential 3 distribution with a mean of 4 minutes. (a) Construct the rate diagram for this queueing system. (b) Find the steady-state probability distribution of the number of cars at the station. (c) Find the expected waiting time (including service) for those cars that stay.
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