best books on probability

Seventh Chapter parameter estimation Content Summary: One, point estimate 1, set for the overall sample, the overall distribution function is known as the parameters to be evaluated for the corresponding sample observations. The problem of point estimation is to construct an appropriate statistic and estimate the value of the parameters to be evaluated with its observations. Here is called the estimate, called the estimated value, both of which are collectively estimated. This is called the poin

variables can be listed at most, the random variables are called discrete random variables. 2. Distribution law of discrete random variables (1) Definition: All possible values of discrete random variables and the probability value when taking each value, called discrete random variable distribution law, expressed as Or in a tabular representation: X1 X2 ... xn ... Pk P1 P2 ... pn ... or recorded as ~ (2) Nature:, Note: This property is a suffici

distribution of random variables, is called a finite pair or an infinite set of two-dimensional random variables. The distribution function of two-dimensional discrete random variables is: 5, for a two-dimensional random variable distribution function, if there is a nonnegative integrable function for any real number has is called a continuous two-dimensional random variable, a function called the probability density of a two-dimensional random vari

2.1 Probability density function2.1.1 DefinitionSet P (x) as the probability density function of the random variable x in the interval [a, b], p (x) is a nonnegative function and satisfiesNote the difference between probability and probability density function.Probability is the area of the corresponding area under the

Transfer from http://outofmemory.cn/wr/?u=http%3A%2F%2Fwww.gocalf.com%2Fblog%2Funbalanced-coin.htmlUsing equal probability Rand5 to generate equal probability Rand3The problem itself is very clear, but do not know what the topic is good, let's say so first.Problem Description: There is now a function called Rand5, which can generate a random integer in the range of [0, 5) equal

PHP winning probability algorithm, winning probability algorithm We first completed the background PHP process, the main work of PHP is responsible for the allocation of prizes and the corresponding probability of winning, the current page click to flip a block will want to background PHP to send AJAX requests, then the background PHP based on the

We still use the "Student Network" as a sample, 1.Figure 1First, the intuitive interpretation of causal judgment (causal reasoning) is given.To figure it out.That is, the probability of a student getting a good recommendation is about 0.5.But suppose we know that students have a lower IQ. Then the probability of getting a good letter of recommendation is reduced:Further. Assuming that the exam is very diffi

false" the error, uses the expression to make the first kind of mistake the probability, namely {}; (2) When the hypothesis H0 actual error, by the sample observation value made to accept the H0 error conclusion, called the second type of error or "false" error, with the expression of the probability of committing the second type of error, that is {}; When the sample capacity is fixed, to reduce the

PHP probability calculation function summary, php probability function. Summary of PHP probability computing functions. php probability functions are actually useless in this blog. it's too simple for people to think about it. no one else can think about it. But looking at the summary of PHP

Php winning probability algorithm and winning probability algorithm We will first complete the PHP process in the background. The main task of PHP is to configure the awards and the corresponding winning probability. When the front-end page clicks a box, we will want PHP to send ajax requests in the background, then, based on the configuration

PHP probability calculation function summary, php Probability Function In fact, this blog is useless. It's too simple. People will not be able to think about it, and even people will think about it. But it's really bad to watch my blog for so long ~. In the next article, only the code of hydrology occupies at least 10 KB of OSC database space. This is a classic probabi