Probability theory, how is it calculated here, and the detailed steps?

e's -(x+y) is e's -x times multiplied by e's -y.

Then, if you integrate y, you can take the -x power of e.

That is, multiply e e to the power of -x (the -y power of e to the y integral) because the -y power of e to the y integral gives the result of the negative -y power of e. The upper bound is positive infinity and the lower bound is 0, so the integral result is 1

So. The -x power of e is multiplied by (the -y power of e is integrated by y) and the -x power of e is multiplied by 1

e to the -xth power.

I hope I've explained it more clearly.

Probability theory and mathematical statistics are used to get high scores.

The basic formula should be mastered.

First of all, you must be able to calculate the classical probability, which can be solved with the knowledge of high school mathematics, if you are weak in solving classical probability, you should systematically review the probability knowledge in high school mathematics, and you must do each type of probability solving problem, although it may not be tested, but it is also necessary to prevent accidents, and prepare for the later review.

Random events and probability are the first chapter of probability statistics, and they are also the basis of the following content, and the basic concepts and relationships must be clearly distinguished. Conditional probability, full probability formula and Bayesian formula are the focus, and in addition to the classical probabilities mentioned above, Bernoulli generalizations and geometric generalizations should also be focused on mastering.

The second chapter is random variables and their distributions, first of all, the concept and properties of random variables and their distribution functions should be understood, and the common discrete random variables and their probability distributions: 0-1 distribution, binomial distribution b(n,p), geometric distribution, hypergeometric distribution, Poisson distribution p( ) The concept of continuous random variables and their probability density; Uniform distribution u(a,b), normal distribution n(,2), exponential distribution, etc., their properties and characteristics should be clearly remembered and skillfully applied, and they are often involved in the exam questions.

Chapter 3 is multidimensional random variables and their distributions, mainly two-dimensional. The contents of the examination specified in the syllabus are: probability distribution, marginal distribution and conditional distribution of two-dimensional discrete random variables, probability density, marginal probability density and conditional density of two-dimensional continuous random variables, independence and non-correlation of random variables, distribution of commonly used two-dimensional random variables, and distribution of simple functions of two or more random variables.

The fourth part is the numerical characteristics of random variables, which is not difficult to grasp, mainly to memorize some relevant formulas and the numerical characteristics of common distributions. The law of large numbers and the central limit theorem are also based on memorization on the basis of understanding, and can be easily solved with relevant exercises.

Grasp the focus of the common exam.

The examination of this part of mathematical statistics is not very difficult, first of all, the basic concepts are clearly understood. 2. Be familiar with the concepts and properties of distribution, t-distribution and f-distribution, which are often covered in the exam questions. The moment estimation method and the maximum likelihood estimation method for parameter estimation should be focused on verifying the unbiased estimation of the estimator.

There are not many hypothesis tests, but as long as they are stipulated in the syllabus, they should not be ignored. The basic idea of significance testing, the basic steps of hypothesis testing, the two types of errors that can be produced by hypothesis testing, and the hypothesis testing of the mean and variance of a single and two normal populations are the test points.

Three probability superposition calculations:ABC three events, as evidenced by the Tracen P (AUBUC).

Let d = aub, p (aubuc) = p (duc) = p (d) + p (c) - p (dc). Command.

p(d)=p(a)+p(b)-p(ab)。

p(dc)=p(acubc)=p(ac)+p(bc)-p(abc)。

Probability. is a numerical measure of the likelihood of a chance event occurring. Suppose after many repeated experiments (represented by x) and several times by chance (represented by a) occur several times (represented by y).

With x as the denominator and y as the numerator, a numerical value (represented by p) is formed. In the multiple posture tests, p is relatively stable at a certain value, and p is called the probability of a occurrence. If the probability of a chance event is determined by long-term observation or a large number of repeated experiments, then such probability is statistical or empirical.

The problem is that in "Other", the density function should be 0, not 1

The results of the calculations are as follows:

The calculations are just too cumbersome.

The solution process is shown in the following figure:

The first question is a =1000

Second question =1 25

The third question y obeys b (5, 1, 25).

Fourth question p=1-(24, 25) 5