On any given day my mood can be in one of three states: happy, sad, or morose. If I am happy on a given day, then on the next day I will be happy 80% of the time, sad 15% of the time, and morose 5% of the time. If I am sad on a given day, then on the next day I will be happy 50% of the time, sad 20% of the time, and morose 30% of the time. If I am morose on a given day, then on the next day I will be happy 40% of the time, sad 40% of the time, and morose 20% of the time. Given that I am sad today, find the probability that I will be in each of t

On any given day my mood can be in one of three states: happy, sad, or morose. If I am happy on a given day, then on the next day I will be happy 80% of the time, sad 15% of the time, and morose 5% of the time. If I am sad on a given day, then on the next day I will be happy 50% of the time, sad 20% of the time, and morose 30% of the time. If I am morose on a given day, then on the next day I will be happy 40% of the time, sad 40% of the time, and morose 20% of the time. Given that I am sad today, find the probability that I will be in each of t

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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ne bets $1. 0.45, he wins the game and with probability 1 - p = 0.55, he loses the game. His goal is to increase his capital to $3, and as soon as he does, the game is over. The game is also over if his capital is reduced to zero. Construct an absorbing Markov chain and answer the following questions. • What is the expected duration of the game? • What is the probability that he goes broke?
The main topic is Markov Chains:Students in Geology class never know what is going to happen in the class, as the teacher may: give them a pop quiz, take them to field practice, analyze the topic of the day, or lecture on a special topic.If one day there is a test, the next day there is always a field practice.If one day there is field practice, the next day there is no practice or test, but there is still a chance of the day's topic or special lecture.of the day or of the special lecture.If on a certain day the topic is tested, the probabilities for the next day are ¼ for the test, 1/6 for the topic and 1/3 for the lecture.and 1/3 for the lecture.If one day there is a lecture, the odds for the next day are ¼ for the test, 1/8 for the practice, 1/8 for the topic analysis and ½ for the lecture.for the analysis of the topic and ½ for the lecture.One of the students has calculated that they can expect quizzes 43/287 of the lecture days; field practice72/287 of the class days; topic…
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