first course in probability

1. a random number generator generates 0 with probability P and 1 with probability (1-p). How to generate equal probability 0 and 1? If the random number generator is used to generate two bits, the probability of occurrence of 00 is, the probability of occurrence of 01 is,

Description After 4 years 'waiting, the game "Chinese Paladin 5" finally comes out. tomato is a crazy fan, and luckily he got the first release. now he is at home, ready to begin his journey. but before starting the game, he must first activate the product on the official site. there aretoo implements passionate fans that the activation server cannot deal with all the requests at the same time, so all the players must wait in queue. each time, the server deals with the request of the first playe

Understanding probabilities with the entity-Contact point of view:Each variable is associated with an event, and the variable is dependent on the existence of the event, and two entities are one-to-two connections;Each event is associated with a test, and the event is dependent on the existence of the experiment, and two entities are many-to-one;The set of values for a variable is s, if a mapping table is defined on S, the mapping table satisfies the nature of the

UV-1498 Activation (DP + probability) Description After 4 years 'waiting, the game "Chinese Paladin 5" finally comes out. tomato is a crazy fan, and luckily he got the first release. now he is at home, ready to begin his journey. but before starting the game, he must first activate the product on the official site. there aretoo implements passionate fans that the activation server cannot deal with all the requests at the same time, so all the players

1 random events and their probabilities Trials, EventsRandom events (accidental events), inevitable events, impossible eventsThe properties and algorithms of probability 2 probability Mutex event: Event A and time B cannot occur concurrently, p (a∪b) =p (a) +p (b) multiplication formula: P (AB) =p (b) p (a| BWhen two events are independent, p (AB) =p (B) p (a)In general, set N events a 1, a 2,..., a n incom

Maximum likelihood estimation MLE Given a bunch of data, if we know that it was randomly taken out of a certain distribution, we don't know the specific parameter of the distribution, i.e. "the model is determined and the parameters are unknown". For example, for linear regression, we assume that the sample is subject to a normal distribution, but we do not know the mean and variance, or for logistic regression, we assume that the sample is subject to the two-item distribution, but we do not kno

This article mainly analyzes the probability of a Python bullfighting game step by step and calculates the probability of a bullfighting game. Interested friends can refer to those coming home from the next year to gather together with friends and family, mahjong, landlords, and bullfights are often used at meetings. In these games, bullfighting is the most popular because it can be played by many people wi

Learning notes TF009: logarithm probability regression, learning notes tf009 The logistic function, also known as the sigmoid function, is a probability distribution function. Given a specific input, calculate the probability of output "success" and the probability of "Yes" to the reply question. Accept a single input.

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 probability of configuration, through the probability algorithm to give the winn

This is a little bit of understanding about the probability of re-learning after N years of graduation. It takes a lot of time and tragedy to return to school... Therefore, students should hurry up at school to consolidate their foundations. ArticleThe content is manually typed by yourself. It is a little bit of Study Notes (too lazy to write). It is not necessarily correct. You are welcome to discuss it. If there is anything wrong, please point it

Ivan and microhard agreed to use a simpler criteria --- Ivan shocould find at least one bug in each subsystem and at least one bug of each category. Macrosoft knows about these plans and it wants to estimate the time that is required for Ivan to call its program disgusting. it's important because the company releases a new version soon, so it can correct its plans and release it quicker. nobody wocould be interested in Ivan's opinion about the reliability of the obsolete version. A bug found in

I. PGM Figure from: http://blog.sina.com.cn/s/blog_5980285201011z75.html Ii. Reasoning Based on the probability graph model. Example: For example, if a message is sent through a noisy channel, the information is composed of 0 and 1. Due to the noisy, each bit has a probability of 20% error. Due to the characteristics of the sent signal, the probability of 1 fol

1. birthday paradox How many people must be in a room to make the chance of two people having the same birthday reach 50%? 1) Probability Analysis Assume n = 365 days a year, The probability that two people's birthdays fall on a fixed number of days R is 1/N * 1/n = 1/N ^ 2 The probability of two people's birthdays falling on the same day is N * 1/N ^ 2 = 1/n Not

Test instructionshave s system, n kinds of bugs, Xiao Ming every day to find a bug, may be any one system, may be any kind of bug, that is, a system bug probability is 1/s, is a certain bug probability is 1/n.Ask him to find the bug,n of the s system, the desired number of days.AnalysisCalculate expected e=∑ all possible days * probabilitiesFind s system n bug, need minimum max (s,n) days, and the possible

Weather conditionsTime limit:2000/1000 MS (java/others) Memory limit:65536/32768 K (java/others)Total submission (s): 638 Accepted Submission (s): 257Problem description If we divide the weather into rainy days, cloudy and sunny 3 kinds, the probability of conversion between a given variety of weather, such as rainy day conversion to rainy days, cloudy and sunny the probability of 0.4,0.3,0.3 respectively.

This article mainly introduces Python's use of the random and tertools modules to solve some classic probability problems. This article describes the use of the random and tertools modules to solve the problems of goat door, playing cards, and birthday paradox, for more information, see Common functions in the random module The code is as follows: Random ()Returns a real number within the range [0, 1;Uniform (a, B)Returns a real number in the range [

Python uses the random and tertools modules to solve some typical Probability Problems. Common functions in the random ModuleCopy codeThe Code is as follows:Random ()Returns a real number within the range [0, 1;Uniform (a, B)Returns a real number in the range [a, B;Randint (a, B)Returns an integer in the range [a, B;Choice (sequence)Returns an element in the sequence. The sequence is an ordered sequence, such as list, string, or tuple;Randrange ([star

Markov process: The Markov process is divided into three kinds according to whether the state and time parameters are continuous or discrete: 1. The time and the state are all discrete called Markov chains, 2. Time and state are called Markov processes continuously, 3. Time continuous, state discrete Markov chain called continuous time. The Markov process is characterized in that the state of the process in the T-time (T>T0) is related only to the moment T0 when the process is in a known condit

Maximum likelihood estimation MLE Given a bunch of data, if we know it is randomly taken out of a distribution, we do not know the specific parameters of the distribution, that is, "the model has been set, the parameter is unknown." For example, for linear regression, we assume that the sample is subject to a normal distribution, but does not know the mean and variance, or for logistic regression, we assume that the sample is subject to two-item distribution, but does not know the mean, the logi

SGU495 Kids and Prizes probability DP, expected Formula Question After this question is first entered, there is no place to submit it. The first SGU question can only be submitted on HUSTOJ. There are n boxes in which there are gifts. m people, each person takes them. After they take the gift, they take it out and put it back, hoping to select the number of gifts. In fact, at the beginning, we assume that the equation dp [I] is the