first course in probability

I. Classical and geometrical approximate 1.1 classical and geometrical approximate features 1) in common: equal probabilities (the probability of each occurrence being the same) 2) difference: The classical approximate sample space is a finite set. A geometric profile can be an infinite set, but it can be represented by a geometric region 1.2 equation 1) Classical Overview: The number of basic events known as N and the result of the

of the current winning member. Worst case In the worst case, we hire every candidate, M = n. Probability Analysis In fact, we neither know the order in which candidates appear nor control this order, so we use probability analysis. Probability Analysis is to use probability Technology in problem analysis. To use

Zheng @ playfun SD 1: "There is a big difference between people. At the same time, there is little difference between people, sometimes just a little bit. A person's abilities can be divided into several levels: knowledge, meeting, and energy. A person can do things in several realms, such as hitting, gambling, and fighting. After learning a lot of knowledge, it does not mean that you will solve the problem and seize the opportunity. Learning these skills does not mean that you have in

Topic Link: Click to open the linkTest instructionsThere are n kinds of cards, every packet of instant noodles have a certain probability to get one of the cards (may also not get cards)Ask about the expectations of the number of instant noodles that the dragon needs to eat.Ideas:Dp[i] means that you already have a card that has a status of I, how many packages are needed to have all the cards,Apparently dp[(1And the answer is dp[0];Using example two

Title Link: http://acm.zjut.edu.cn/onlinejudge/problem.php?cid=1101pid=8Surface: Problem I:no2 Time limit: 1 Sec Memory Limit: MB Submit: 342 Solved: 23 [Submit] [Status] [Web Board] DescriptionKnown to have a city of n people, the probability of having a zombie disease is p. You go to the test and check it out is positive. The doctor told you this test, the person who has the disease detects positive

Maximum probability selection to "Best Girl" algorithmLet's say you're a boy, and God has 20 girls for you when you're 20-30 years old. These girls are willing to be your partner, but you can only choose one of them. The following conditions are selected:1. For you, these 20 girls can be sorted, that is, you can rank the quality of them afterwards, the first girl is the best for you, the 20th is the worst for you.2. The 20 girls do not appear in your

? Algorithm analysis: An interesting question: First of all, I subconsciously think that I should first take a look at the comparison, but I don't want the best. Later, I saw on the Internet that the probability of such a strategy is quite high, first, review the complete online answer: Policy 1: Draw lots in advance and select the number one. For example, if the number of girls reaches 10th, the 10th girls who appear in your life will be identified

Title 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 decided to resign to fate ...Specifically, small z to this n socks from 1 to n number, and then from the number L to R (L Although small z does not care about two socks is not a complete pair, even do not care about two socks whether a left and right, he is very conce

Probability question .. You can use either DP or formula. Abstract questions: There are n small balls, and the expected number of retrieved small balls is retrieved m times. DP maintains the two States. The first retrieved is the probability of a ball that has not been taken out. DP [I] and the probability of a ball that has been taken out is NP [I]; If the secon

. Idea: The question requires Cong to keep approaching Coco. And keep the label as small as possible. Then we can use spfa to pre-process POS [I] [J]. Pos [I] [J] indicates that the shortest path from vertex I to vertex J is adjacent to vertex I and has the smallest vertex number. That is, when Cong is at the scenic spot I and Coco is at the Scenic Spot J, Cong will go to the scenic spot number in step 1. Thank you for your explanation of spfa! DP [I] [J] indicates that Cong is at vertex I, and

Consider an event, which has two results with equal probability. For example, if a coin is thrown, the chances of front and back are equal. Now we want to know how long it will take for me to get a specific sequence if I keep throwing coins. Sequence 1: Negative, positive, and negativeSequence 2: Negative, positive, positive First, I threw a coin repeatedly until the last three throwing results form sequence 1. Then I wrote down how many times I threw

In addition to precise reasoning, we also have the means to solve the distribution of a single variable in a probability graph by non-precise inference. In many cases, the probability map can not be simplified into a cluster tree, or simplified the number of random variables in a single regiment after the formation of a cluster, resulting in the efficiency of the mission tree calibration is low. As an examp

PHP array according to the probability returned algorithm now has a 9 key array: $ arrarray (, 9); I want: 1's return probability is 30% 2's return probability is 20% 3's return probability is 10% 4's return probability is 50% others no matter how this algorithm calculates -

1, Probability density function In classifier design (especially Bayesian classifier), when the prior probability of a class and the probability density of a class are both known, determine the discriminant function and decision plane according to certain decision rules. However, in practice, the probability density o

The important concepts in probability theory Random variablesdistribution function, density functionNumerical characteristics of random variablesThe relationship between random variables Randomised trials Random Event A B C Inevitable Events Oh Miga Impossible Event Empty Basic events for random events Composite Event Basic Events The set of all possible results of the random experiment E is called the sample null Ω, and any subset of the sample sp

The big turntable is one of the most interesting items in many online activities recently. Let's take a look at the algorithm and example of the winning probability of the big turntable. I hope it will help you. The big turntable is one of the most interesting items in many online activities recently. Let's take a look at the algorithm and example of the winning probability of the big turntable. I hope it w

3.1 Two-Point Distribution and even distribution1. Two-Point DistributionMany random events have only two results. If the result of the product is qualified or unqualified, the product or reliable work may fail. This type of random event variable has only two values. Generally, 0 and 1 are used. It follows two-point distribution.Its probability distribution is:Where Pk = P (X = Xk) indicates the probability

In machine learning, we are usually interested in determining the best assumptions in hypothetical space H Given the training data D .The so-called best hypothesis, one approach is to define it as the most probable (most probable) hypothesis under the knowledge condition of the prior probabilities of different assumptions in the given data D and H .Bayesian theory provides a direct way to calculate this possibility. More precisely, the Bayes rule provides a method for calculating hypothetical pr