The Emergence and Development of Probability Theory and Mathematical Statistics

The difference and relationship between probability theory and mathematical statistics: probability theory is the foundation of mathematical statistics, and the main content is probability theory plus a little bit of the most basic mathematical statistics; Mathematical statistics, on the other hand, mainly focuses on parameter estimation, hypothesis testing, regression analysis, variance estimation, and experimental design. Differences and connections between probability theory and mathematical statistics:

Probability theory is a branch of mathematics that studies the quantitative law of random phenomena, and is a study of the probability of things happening, so probability theory includes unit events, event space, random events, etc., in addition, probability theory is widely used in natural sciences, economics, medicine, finance and insurance and even humanities; Mathematical statistics is a branch of mathematics, which is divided into descriptive statistics and inferential statistics, and the development of mathematical statistics can be roughly divided into three stages: the classical period, the modern period and the modern period, and the main contents of mathematical statistics include parameter estimation, hypothesis testing, correlation analysis, experimental design, non-parametric statistics, process statistics, etc.

Probability theory and mathematical statistics are very important disciplines in mathematics, and they are commonly used mathematical tools in scientific research. The following is a simple understanding of probability theory and mathematical statistics.

Probability theory is a mathematical discipline that studies the occurrence of random events and their laws. The main research is on the probable family origin rate and its properties of random events. It has two core concepts:

Experiments and events. A trial is the observation and testing of an event, and an event is a possible outcome in an experiment. The main contents of probability theory research include:

Random variables, probability distributions, probability densities, conditional probabilities, and Bayes' theorem, among others.

Mathematical statistics is a discipline that infers general laws from sample data. It uses statistical methods to study the nature and laws of random phenomena, and to provide support for practical problems and decisions. The main research contents of mathematical statistics include:

Sampling distribution, parameter estimation, hypothesis testing, and ANOVA, etc.

Probability theory and mathematical statistics are widely used, involving many fields such as economics, finance, medicine, environment, and engineering. In economics, probability theory and mathematical statistics are widely used in risk management and investment decision analysis in financial markets. In the field of medicine, probability theory and mathematical statistics can be used to analyze disease epidemic trends and test the efficacy of drugs.

In the field of environment and engineering, they can be used to build mathematical models of the city, weather and environmental pollution, etc.

Summary. Hello, Probability Theory and Mathematical StatisticsProbability theory and mathematical statistics are probability theory and mathematical statistics

Hello, Probability Theory and Mathematical StatisticsProbability theory and mathematical statistics are probability theory and mathematical statistics

Chinese-to-English translation skills are the act of transforming information in one language into another on the basis of accuracy and fluency. Translation is the process of transforming a relatively unfamiliar expression into a relatively familiar one.

1. The method of addition and translation refers to adding some words, short sentences or sentences in translation according to the different ways of thinking, language habits and expressions of English and Chinese, so as to more accurately express the meaning contained in the original text.

2. Provincial translation methodThis is a translation method corresponding to the additional translation method, that is, to delete words that do not conform to the thinking habits, language habits and expressions of the target language, so as to avoid redundant translations. The opposite is true for example sentences of the additive method.

3. The conversion method refers to the conversion of the word class, sentence structure and voice in the original sentence in order to make the translated text conform to the expression, method and habits of the target language during the translation process.

Fourth, the split syntax method and the merging method are two corresponding translation methods. Syntax splitting is the process of splitting a long and complex sentence into several shorter, simpler sentences, which is usually used to translate from English to Chinese. The merging method is to merge several short sentences into one long sentence, which is generally used to translate from Chinese to English.

Not strictly speaking, the two are in opposite directions.

For example, if you already know that the random variable x is a normal distribution and that it is n(0,1), you can deduce its numerical characteristics such as expectation and variance, and some other properties of it, and what is the distribution of the square of x, and what is the distribution of adding to another random variable y. These works fall under the category of probability theory.

If there is a random variable z in practice, you don't know what the distribution is, you see some test values, you think it may be a normal distribution, so you assume that it is a normal distribution, you use the test data, you deduce that its mean value may be 1, the variance may be 4, and then do a hypothesis test to see how reliable this conclusion is, if you think it is reliable, use this conclusion to do the analysis, or ** the results of the test that will be conducted. It's called statistics.

Statistics is based on probability, and statistical inference and hypothesis testing should be based on the idea of probability.

In the past, the thinking was simple and naïve, but the thinking of the later industry has become mature, and the understanding of things has become clearer, and it should be said that it is the transformation from phenomenon to essence.

What is the name of the textbook? It's a book about probability, because probability and statistics are inextricably linked

One is theory, the other is practice.

1. Use the full probability formula.

Specific steps: set up the output of A, B and C factories as A1, A2, A3; Set the defective rate of A, B and C b1, b2, b3

That is, the defective rate is b.

p(b)=p(a1)p(b1|a1)+p(a2)p(b2|a2)+p(a3)p(b3|a3)

p(b1|a1)= ;p(b2|a2)= ;p(b3|a3)= substituting the previous formula gives p(b)=

2. Use the Bayesian formula.

This problem can be solved using the full probability formula and the Bayesian formula, respectively

2。(40%*3%) (35%*4%+40%*3%+25%*2%) calculation should not be a problem, I hope it will be helpful to the landlord.