MS/Sheldon M. Ross-Introduction to Probability Models, Tenth Edition (). pdf. Find file Copy path. Fetching contributors Cannot retrieve contributors at. DRM-free (PDF, Mobi, EPub) Introduction to Probability Models, Tenth Edition, provides an introduction to elementary probability theory and stochastic. Introduction to. Probability Models. Ninth Edition. Sheldon M. Ross. University of California. Berkeley, California. AMSTERDAM • BOSTON • HEIDELBERG •.
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Introduction to Probability. Models. Tenth Edition. Sheldon M. Ross. University of Southern California. Los Angeles, California. AMSTERDAM • BOSTON. Theoretical basis for stochastic processes and their use as models of real-world phenomena. Topics include Markov chains, Poisson processes, Brownian motion and stationary processes. Applications include Gambler's Ruin, birth and death models, hitting times, stock option pricing. Introduction to Probability Models Tenth Edition This page intentionally left blank Introduction to Probability Models Tenth Edition Sheldon M. Ross University of.
Skip to search form Skip to main content. Ross Published Prerequisites: Theoretical basis for stochastic processes and their use as models of real-world phenomena. Topics include Markov chains, Poisson processes, Brownian motion and stationary processes. Applications include Gambler's Ruin, birth and death models, hitting times, stock option pricing, and the BlackScholes model. View Paper. Save to Library.
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And hopefully you are going to develop this skill during this class. Now, I could spend a lot of time in this lecture talking about why the subject is important.
I'll keep it short because I think it's almost obvious. Anything that happens in life is uncertain. There's uncertainty anywhere, so whatever you try to do, you need to have some way of dealing or thinking about this uncertainty. And the way to do that in a systematic way is by using the models that are given to us by probability theory. So if you're an engineer and you're dealing with a communication system or signal processing, basically you're facing a fight against noise.
Noise is random, is uncertain. How do you model it?
How do you deal with it? If you're a manager, I guess you're dealing with customer demand, which is, of course, random. Or you're dealing with the stock market, which is definitely random. Or you play the casino, which is, again, random, and so on. And the same goes for pretty much any other field that you can think of. But, independent of which field you're coming from, the basic concepts and tools are really all the same.
So you may see in bookstores that there are books, probability for scientists, probability for engineers, probability for social scientists, probability for astrologists. Well, what all those books have inside them is exactly the same models, the same equations, the same problems.
They just make them somewhat different word problems. The basic concepts are just one and the same, and we'll take this as an excuse for not going too much into specific domain applications.
We will have problems and examples that are motivated, in some loose sense, from real world situations. But we're not really trying in this class to develop the skills for domain-specific problems. Rather, we're going to try to stick to general understanding of the subject.
So the next slide, of which you do have in your handout, gives you a few more details about the class. Maybe one thing to comment here is that you do need to read the text. And with calculus books, perhaps you can live with a just a two page summary of all of the interesting formulas in calculus, and you can get by just with those formulas.
But here, because we want to develop concepts and intuition, actually reading words, as opposed to just browsing through equations, does make a difference. In the beginning, the class is kind of easy. When we deal with discrete probability, that's the material until our first quiz, and some of you may get by without being too systematic about following the material.
But it does get substantially harder afterwards. And I would keep restating that you do have to read the text to really understand the material. So now we can start with the real part of the lecture. Let us set the goals for today. So probability, or probability theory, is a framework for dealing with uncertainty, for dealing with situations in which we have some kind of randomness. So what we want to do is, by the end of today's lecture, to give you anything that you need to know how to set up what does it take to set up a probabilistic model.
And what are the basic rules of the game for dealing with probabilistic models? So, by the end of this lecture, you will have essentially recovered half of this semester's tuition, right? So we're going to talk about probabilistic models in more detail-- the sample space, which is basically a description of all the things that may happen during a random experiment, and the probability law, which describes our beliefs about which outcomes are more likely to occur compared to other outcomes.
Probability laws have to obey certain properties that we call the axioms of probability. So the main part of today's lecture is to describe those axioms, which are the rules of the game, and consider a few really trivial examples. OK, so let's start with our agenda. The first piece in a probabilistic model is a description of the sample space of an experiment. So we do an experiment, and by experiment we just mean that just something happens out there.
And that something that happens, it could be flipping a coin, or it could be rolling a dice, or it could be doing something in a card game. So we fix a particular experiment. And we come up with a list of all the possible things that may happen during this experiment. So we write down a list of all the possible outcomes. So here's a list of all the possible outcomes of the experiment. I use the word "list," but, if you want to be a little more formal, it's better to think of that list as a set.
So we have a set. That set is our sample space. And it's a set whose elements are the possible outcomes of the experiment. So, for example, if you're dealing with flipping a coin, your sample space would be heads, this is one outcome, tails is one outcome.
And this set, which has two elements, is the sample space of the experiment. What do we need to think about when we're setting up the sample space? First, the list should be mutually exclusive, collectively exhaustive. What does that mean? Collectively exhaustive means that, no matter what happens in the experiment, you're going to get one of the outcomes inside here.
So you have not forgotten any of the possibilities of what may happen in the experiment. Mutually exclusive means that if this happens, then that cannot happen.
So at the end of the experiment, you should be able to point out to me just one, exactly one, of these outcomes and say, this is the outcome that happened. So these are sort of basic requirements. There's another requirement which is a little more loose. When you set up your sample space, sometimes you do have some freedom about the details of how you're going to describe it. And the question is, how much detail are you going to include?
So let's take this coin flipping experiment and think of the following sample space. One possible outcome is heads, a second possible outcome is tails and it's raining, and the third possible outcome is tails and it's not raining.
So this is another possible sample space for the experiment where I flip a coin just once.
It's a legitimate one. These three possibilities are mutually exclusive and collectively exhaustive.