Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of these outcomes is called an event.
Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes, which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion.
Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability theory describing such behaviour are the law of large numbers and the central limit theorem.
As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics or sequential estimation. A great discovery of twentieth-century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics.
Hi all. I am searching for a good textbook on probability theory. I finished my B.S. in mathematics last fall and have covered real analysis and abstract algebra so I want a book that goes into actual mathematical theory and not just a basic book about probability like you would learn in...
Homework Statement
A - something that is a known possibility
C - correct conditions conducive to produce A
T - many trillion years in which C continues
Homework Equations
Is it true that with the above factors the probability of "A" is "1", or very close to 1?
The Attempt at a...
Homework Statement
The rv X has pdf f(x) = cx, for 1 < x < 2, with f(x) = 0 otherwise. Compute the 3 M’s, and also compute the minimized risks in each case. Mode, median, mean.
Homework Equations
The Attempt at a Solution
I think I have computed the 3 M's
mode of x = 2
median...
Hi all,
I've got this very simple problem:
I know it is an elementary problem, but I never really got into that bayes' theorem, which I need to use here, right? I would be grateful for simple and plain explanation.
thanks for your time,
rahl.
Homework Statement
Now you and your fiend play a different game. You flip your coin until it comes up heads the first time. Let X denote the number of flips needed. Your friend rolls its die until it comes up "3" or "5". The first try let Y denote the number of rolls needed. Assume X and Y are...
I'm interested in learning the calculus of general random variables, i.e. those that do not necessarily have a density or mass function - such as mixtures of continuous / discrete / Cantor-type variables.
There seem to be several different approaches:
1. Via densities, using delta...
According to Cantor, http://books.google.com/books?id=Er1r0n7VoSEC&pg=PA98&dq=plane+line+cardinality+%22set+theory%22&as_brr=0" example).
Do you see the contradiction |R| = |R2| vs. |R|/|R2| = 1/∞? Am I missing something?
i am working on theoretical physics
i hope i can get a book on probability theory
i hope this book is a bit advanced to have detailed discussion of characteristic functions and their applications.
i do not like the statistics applications. I hope that part is as small as possible...
i have to study following topics in probability theorem and iam totally a beginner so please suggest me a book
Probability, conditional probability, random variables, Expected Value, Specific discrete and continuous distributions, e.g. binomial, Poisson, geometric, Pascal, hypergeometric...
Dear all,
I have a question.
Suppose we have 3 events X,Y,Z defined as having 200 heads, 400 heads & 600 heads obtained in tossing a fair coin for 800 times.
Then, P(Z)=P(X+Y)=P(600)=P(200+400)=P(X)+P(Y)=P(200)+P(400)
The answer is false but I view it otherwise. My argument is based...
Homework Statement
http://img291.imageshack.us/img291/4844/14820448wb9.png
The Attempt at a Solution
First of all I'm trying to find the expected time of a cycle. In a cycle two things can happen:
1) the car lives long enough to reach A with probability 1-F(A)
2) the car fails to...
My background is calculus through differential equations and linear algebra at a community college. How hard is an intro to probability theory at a school like UCLA?http://www.math.ucla.edu/ugrad/courses/math170ab/170Aoutline.shtml I'm thinking about taking it this fall.
What book should I get to learn probability theory by self-study? I bought Shiryaev's Graduate Text in Mathematics and the problem is that it just develops so much theory but then provides few exercises, making it really hard to self-study. I probably should have expected this though. So, I am...
I'm interested in published papers, if any, addressing the issue of whether Bell type experiments can be explained simply with classical, epistomological probability theory. In particular, can the expected "quantum" result (i.e. the probability that photons A and B will both pass through their...
Homework Statement
An individual traveling on the real line is trying to reach the origin. However, the larger the desired step, the greater is the variance in the result of that step. Specifically, whenever the person is at location x, he next moves to a location having mean 0 and variance...
An individual traveling on the real line is trying to reach the origin. However, the larger the desired step, the greater is the variance in the result of that step. Specifically, whenever the person is at location x, he next moves to a location having mean 0 and variance \beta x^2. Let X_n...
Hello There,
this is my first post. I would like an information: Which is the basic way to prove probability theory?.. I mean prove the probability that a situation in influenzed from the situation before and/or calculate the probability that in n it will have a determinate situation...??
How...
If A and B are independent, prove that \bar A , \bar B are independent.
Could someone help me start this. It's due tomorrow. I managed to prove that \bar A [/tex] is independent with B and that \bar B is independent with [itex] A , but I can't get the last one (the question I put...
Homework Statement
A die is loaded so that the numbers 2 through 6 are equally likely to appear but that 1 is 3 times as likely as any other number to appear. What is the probability of getting an even number?Homework Equations
This is where I become lost - I'm not sure how to get the...
Question:
Deer ticks can carry both Lyme disease and human granulocytic ehrilichiosis (HGE). IN a study of ticks in the Midwest, it was found that 16% carried Lyme disease, 10% had HGE, and that 10% of the ticks that had either Lyme disease or HGE carried both diseases.
(a) What is the...
Question:
Find out the birthday (month and day but not year) of a randomly chosen person. What is the sample space of the experiment. How many outcomes are in the event that the person is born in July?
Attempt:
We first must define the sample space. This is how I did it,
S = {JAN1...
EDIT: Please disregard, or delete.
I got it.
Stumped on this question:
Shuffle a deck of cards and turn over the first card. What is the sample space of this experiment? How many outcomes are in the event that the first card is a heart?
Attempt at a solution:
D = \{ deck of 52...
Probability theory...
So we were given some practise problems for the exam...
in it, we got a question that we have NEVER seen in class nor can I find it in the textbook.
The question is:
Find P(min(X, Y ) > x) and hence give the probability density function of U =
min(X, Y ).
Okay...
A Question Reads: "Suppose that the random Variable X is the number of failures before the first success in a series of independent Bernoulli trials with success probability p"
a) derive the probability mass function of X
b) what is the probability that X < x where x is a positive integer...
Hey.. I am having some problems with this homework question, i thought perphaps somebody can help me on it.
-- Let X be a random variable with probability mass function
x P(x)
-1 p
1 1 - p
Find the value of the constant C not equal to 1 such that...
Hello, I was hoping somebody can guide me with this problem, or perhaps help walk me through it. Its for a stats (probability theory) class.
The question reads:
-- Suppose that the probability of exposure to the flu virus during flu season is 0.3. People can get a flu vaccine which...
Hello, I have two questions regarding probaility, i was hoping some body can help me out.
I know that this is a "Physics Forum" However, i thought somebody might still beable to help :)
When rolling 5 distinuishable dice, find the probability that there are two different values?
I did...
Does anyone know if there is any study of probability theory from the point of view of category theory? I was trying to find some references but I just found something about probabilistic automatons and precategories. I would like to see something about probability distributions and categories...