best probability textbook

Consider an event, which has two results with equal probability. For example, if a coin is thrown, the chances of front and back are equal. Now we want to know how long it will take for me to get a specific sequence if I keep throwing coins. Sequence 1: Negative, positive, and negativeSequence 2: Negative, positive, positive First, I threw a coin repeatedly until the last three throwing results form sequence 1. Then I wrote down how many times I threw

Knowledge Points: Bernoulli distribution, two-item distribution, polynomial distribution, prior probability, posterior probability, conjugate distribution, beta distribution, beta-two-item distribution, negative two-item distribution, Dirichlet distribution, gamma function, distributionOne, Bernoulli distribution (Bernouli distribution)Also known as 0-1 distribution, refers to a randomized trial, with only

host picked goat 1. Conversion will win the car. The contestant picked a car and the host picked either of the two goats. Conversion will fail. In the first two cases, contestants can win the car by switching their options. The third case is the only one where contestants win by keeping their original selections. There are two of the three cases that win through conversion selection, so the probability of winning through conversion selection is 2

In addition to precise reasoning, we also have the means to solve the distribution of a single variable in a probability graph by non-precise inference. In many cases, the probability map can not be simplified into a cluster tree, or simplified the number of random variables in a single regiment after the formation of a cluster, resulting in the efficiency of the mission tree calibration is low. As an examp

foundation of mathematics, so that students can not be brought into the right path. At least as a class student, I feel that way. The result is a sense that the course is independent of one area and is very isolated. From some foreign books can be seen, machine learning is actually a multi-disciplinary derivative, and a lot of engineering field theory has a close connection, so that at least let us this beginner can be checked, not feel it is from the stone seam.Next, the

PHP array according to the probability returned algorithm now has a 9 key array: $ arrarray (, 9); I want: 1's return probability is 30% 2's return probability is 20% 3's return probability is 10% 4's return probability is 50% others no matter how this algorithm calculates -

1, Probability density function In classifier design (especially Bayesian classifier), when the prior probability of a class and the probability density of a class are both known, determine the discriminant function and decision plane according to certain decision rules. However, in practice, the probability density o

The important concepts in probability theory Random variablesdistribution function, density functionNumerical characteristics of random variablesThe relationship between random variables Randomised trials Random Event A B C Inevitable Events Oh Miga Impossible Event Empty Basic events for random events Composite Event Basic Events The set of all possible results of the random experiment E is called the sample null Ω, and any subset of the sample sp

efficient without losing fairness. In the case of opaque information, the ghost knows you are the first few lottery, haha. Second, probability lottery The so-called probability lottery is the most easy to think of the lottery algorithm, the probability can be static, it can also be changed in the adjustment, the most difficult is the use of

3.1 Two-Point Distribution and even distribution1. Two-Point DistributionMany random events have only two results. If the result of the product is qualified or unqualified, the product or reliable work may fail. This type of random event variable has only two values. Generally, 0 and 1 are used. It follows two-point distribution.Its probability distribution is:Where Pk = P (X = Xk) indicates the probability

In machine learning, we are usually interested in determining the best assumptions in hypothetical space H Given the training data D .The so-called best hypothesis, one approach is to define it as the most probable (most probable) hypothesis under the knowledge condition of the prior probabilities of different assumptions in the given data D and H .Bayesian theory provides a direct way to calculate this possibility. More precisely, the Bayes rule provides a method for calculating hypothetical pr

parameter of θ produces the above sampling to be expressed asBack to the "model has been determined, parameters unknown," the statement, at this time, we know that, the unknown is θ, so the likelihood is defined as:　　In the actual application is commonly used in both sides to take the logarithm, the formula is as follows:This is called logarithmic likelihood, which is called the mean logarithmic likelihood. And what we call the maximum likelihood is the largest logarithmic average likelihood, n

PHP winning probability algorithm, can be used for scraping cards, large turntable and other lottery algorithm. The usage is very simple, the code has the detailed comment explanation, can understand at a glancePHP/** Classical probability algorithm, * $PROARR is a pre-set array, * Assuming array is: Array (100,200,300,400), * Start is to filter from 1,1000 this probabi