best book on probability

http://www.lydsy.com/JudgeOnline/problem.php?id=2038Learned the next team, quite the orz of GodFirst of all, if you push the formula, it's easy. For query $[l,r]$$ $ans =\frac{\sum \binom{x_i}{2}}{\binom{r-l+1}{2}}$$Late repair ... Come back to mend.#include 　　 DescriptionAs a rambling person, little Z spends a lot of time every morning looking for a pair to wear from a bunch of colorful socks. Finally one day, Little Z can no longer endure this annoying to find socks process, so he decide

First, look at the formula of full probability in the traditional sense: P (B) =∑I=1NP (b| AI) P (AI) The P (B) on the left side of the equal sign is a state amount, and the ∑ on the right is a process amount. This representation is consistent with the representation of the integral: F (n) =∫n0f (x) dx In fact, this process volume superposition into the state of the way is so common, so that you can give a few examples, do not say what Newton-Leibniz

fishing (expect farmers to get the right to license ...). The number of hands above both able to walk and high top of the 2 to do "can go hand not put", but also the crossroads of aaa,222 card to do "Choose the landlord as small as possible probability" The above example can be regarded as a kind of recovery after the game is lost. Why the top 2, not the top K, any one of the steps of the card can be found, this is the actual meaning of the card is t

Title DescriptionXiao Ming is very interested in the probability problem recently. One day, Xiao Ming and Xiao Red play a probability game, first Xiao Ming gives a letter and a word, and then by the small red to calculate the probability that the letter appears in this word. Letters are case insensitive.For example, the given letter is a and the word is Apple, th

In the course of learning Andrew Ng's machine learning, he thought that he had the maximum likelihood estimate, the maximum posterior probability estimate, and the logistic regression, the Bayesian classification of the shutdown was very clear, but after the school pattern recognition course, my outlook on life completely overturned .... Let me give you a word. First of all, the concept of maximum likelihood (MLE) and maximum posterior

5.1 Probability count. Not too clear test instructions. 5.2 (Find an unordered array) the subject will analyze three algorithms that look for a value x in an unordered array a containing n elements. Consider the following stochastic strategy: randomly pick a subscript i, if a[i]=x, then terminate, otherwise, continue to pick a a new random subscript, repeat randomly pick subscript, until we find a subscript j, make a[j]=x, or until we have checked eve

certainly be an error, so I switched to long double, but it was still wrong. I still didn't make it at last. Then I found that the problem can be solved by logarithm. This high school book was read in white .... take the probability of mp [I] [j] and pp [I] [j] As the logarithm log (mp [I] [j]), log (pp [I] [j]), so that the multiplication of the state transition equation can be written as addition. Dp [I]

Document directory Principle 1.1 1.2 example Principle 2.1 2.2 example Principle 3.1 3.2 Example In speech recognition, probability models play a crucial role. Before learning speech recognition technology, you should carefully organize relevant probability knowledge.1. Likelihood Estimation 1.1 Principle In mathematical statistics,Likelihood FunctionA function used to calculate parameters in a st

Probability: Poj 2151 There are t teams and M questions, which give the probability that each team will make each question. Calculate the probability that each team has at least one question and the champion team has at least N questions. Each team has at least one question. The opposite event is that each team has at most 0 questions. Therefore, we need to

Title Description Transmission Door The main problem: a pocket of chocolate, chocolate color has c species. Now take out a chocolate from your pocket, if theChocolate is the same color as chocolate on the table, take two chocolates away, or put the chocolate out on the table.The probability of extracting each color of chocolate from the pocket is equally equal. To remove the n chocolate and the remaining M-G on the tableThe

Deep Learning Book recommendation, deep learning bookAI Bible Classic best-selling book in the field of deep learning! Has long ranked first in Amazon AI and machine learning books in the United States! All data scientists and machine learning practitioners must read books! Recommended by many domestic and foreign experts, such as Tesla CEO Elon Musk! Deep Learning is a branch of machine learning. I

Summary of Probability Theory Relationship between each chapter in probability theory First, the development of mathematics makes our description of the definite phenomenon quite accurate, but there are still some phenomena that are "unclear ", this unclear nature is random. In order to better describe this property probability, the subject

ArticleDirectory Yangche Problems Bayesian inference Yangche Problems The Monty Hall problem, also known as Monti Hall, is a famous probability problem. It originated from a video game: If you are a contestant in a game, there are three closed doors in front of you. One is behind a car, and the other two are behind goats. The host knows the situation behind the door, but you don't know. Your goal is to guess which door is b

Probability:POJ 2151There is a T-team, M-problem, give each team to make each problem probability. Find out that each team has at least one problem and the championship team has at least the probability of making n questions.Each team has at least one problem in the opposite incident is that each team to make at most 0 questions. Therefore, each pair must be asked to make 0 probabilities.The odds of a champ

In the R language, different distributions can be generated for experimentation and learning.In R, the probability function is shaped like ①:where the first letter denotes one aspect of the distribution that it refers to:D = density function (density)p = Distribution functions (distribution function)Q = number of decimal functions (quantile function)R = Generate random number (random deviation)Common probability