first course in probability

EX1:Joey 80% sure he put the missing key in one of the two pockets of his coat. He was 40% sure to put it in the left pocket and 40% OK in the right pocket. If you check the left pocket and find that the key is not found, then what is the condition probability of the key in the right pocket?Analysis: Very basic conditional probability of the problem, the key to solve is to find out which event is the event

;, Which is Bayes's law (Bayesian Law ). This example Example: Five fair coins and ten unfair coins (Head rate: 0.8; Tail rate: 0.2). If you pull a coin, you can drop it for 6 times, and four times you get Head, what is the probability that the coin is fair coin? A: fair coin, B: 4/6 Heads/flips P (B | a) = P (6 flips 4 heads | fair coin) = number of combinations × probability of each combination = 6C4 *

pocket. Every time he needs a match, he takes a match out of a matchbox in any pocket and now has n matches in each of the two boxes of matches, so when he first discovers that one of the boxes is empty, how likely is the other box to have a match of k?Analysis: First of all we need to discuss a point is that the match is located in which pocket of the Matchbox is empty, obviously the left is the right symmetry, we analyze a situation, the square can be.Assuming that the left pocket is empty, t

Two items distributed:Based on the most basic discrete random variable--Bernoulli random variable x, we perform n repetition experiments, the probability distribution result is so-called two-item distribution.Specifically, the probability of a successful experiment is p, and now we do n at this time Yang, set random variable x to indicate the number of successful times of n experiments, then the following d

In the actual problem, we often want to use the existing data to determine whether the occurrence of two events is related. Of course, an angle to find the intrinsic logic of the two events, this angle needs to delve into the nature of the two events, and another angle is the simple method offered by probability theory: based on the probability of two events, we

When we use the basic probability theory to solve practical problems, we can easily find some random variables of the continuous distribution, such as the time of the train station, the life of the lamp, and some time-related random variables, we found it difficult to find out the probability of a point, because the random variable is continuous, The basic event space is an infinite space, and with the infi

In connection with the introduction of discrete random variables, after defining the expected e[x of the random variable x], we tend to focus on the random variable e[g (x) of the function of x in the actual problem, and continue to discuss the expectation of the discrete random variable function, we can easily make the following conjecture:However, we should note that in discrete random variables, because this function relationship g (X) does not change the

Random Variable A random variable is different from a common data variable. It is usually expressed in uppercase letters, such as X, Y, and Z. It is not a parameter but a function, that is, a function. For example, the random variable X indicating whether it is raining tomorrow is shown below. For example, if X = is a vehicle passing through an intersection every hour, a random variable is a description rather than a variable in the equation. There are two types of random variables: discrete an

Based on the concept of instrumental characterization of probabilistic problems, such as random variables, distribution columns, we can begin to discuss a variety of distribution columns. (This chapter is called "Random variables" in the book, but in order to separate from chapter fifth "Continuous random variables", here the title is "discrete Random variable")Poisson distribution derived from the two-item distribution combined series:We are familiar with the two distributions and we are very p

As we've described before, covariance can describe the correlation between two variables to some extent, but sometimes it's not as accurate as the following example:Essentially the same two random variables, the independence is constant, but through this equation I see that if a constant is added to the front of a random variable, the result of the covariance is a relatively large gap, so it is not good for us to measure the independence between the two random variables, So here we standardize t

In discussing the distribution of continuous random variable functions, we can get a simplified version of the model from the general situation (as discussed in the article on normal distribution).Recall the process of solving the function distribution of random variables using the relationship between distribution function and probability density, there is y=g (x), if G (x) is strictly monotonous, then we can use the inverse function to get the range

For God, everything is definite, so probability, as a learning existence, exactly proves human ignorance. Fortunately, humans are still smart enough. We are not at risk because things are random. We decide our actions based on the possibility of things. For example, before a person grabs a bank, he must have repeatedly considered various possibilities. If people wait until everything is confirmed, you may not be able to do anything, because almost eve

determine that you can score 88 points at the end of the course, because you are not the one who gives questions or grades. What happened in the past was actually definite, but it became random because of our ignorance. We dug out a piece of porcelain from somewhere. It may be Confucius's night pot, or it may be Qin Shihuang's tableware, it is also possible that the broken teapot of President Lin's house has been buried in this place from his house t

[Link to this article] Http://www.cnblogs.com/hellogiser/p/random-generator-with-equal-or-unequal-probability.html1. equi probability generation (1) rand5 generate rand3 There is now a Rand5 function that can generate random integers in the range of [0, 5) with equal probability. This function is required to write a Rand3 function (In addition, can no longer use any function or data source that can generate

Original URL: http://m.blog.csdn.net/article/details?id=49130173 first, transcendental probability, posterior probability, Bayesian formula, likelihood function In machine learning, these concepts are always involved, but never really understand the connection between them. Here's a good idea to start with the basics, Memo. 1. Prior probability A priori

following is a visual sense of conditional independence , 9Figure 9There are 2 coins, one just evenly. There is also an uneven and 90% probability of being able to face up. Of course, the two coins look exactly the same.Now let you take out one. Ready to throw 2 times.You throw it first, you find the face up, and you can believe it. The second or front-facing probabili