best probability textbook

Activation Time Limit: 20000/10000 MS (Java/others) memory limit: 32768/32768 K (Java/Others)Total submission (s): 520 accepted submission (s): 179 Problem descriptionafter 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 are too when passionate fans that the activation server can

If you want to use C ++ to generate a random number between 0--n-1, what would you do? You may say that it is very simple. See: Srand (unsigned) Time (null ));Rand () % N; Think about it, is the result random (of course, we do not consider the pseudo-randomness of the Rand () function )? No, because the upper limit of rand () is rand_max. Generally, rand_max is not an integer multiple of n. If rand_max % = r, the probability of a value between 0 and R

Unordered Independent Events Example 1:Flip coins, throwing four times, returns the probability that two times are positive. The probability of all possible arrangements is 2 × 2 × 2 × 2. The number of events that meet the requirements can be listed. However, if the number of throwing events is large, it is impossible. The two sides are placed in four positions. Assume that one is Ha, the other is Hb, and H

that the sample has only one component) from passing 60 to 100 divided into 4 equal intervals of the small window, because X is a one-dimensional vector, will be divided into 4 1 square equals 4 bin, the volume of each bin is recorded as V;B. Statistically, count the number of samples that fall into each bin Ni (which we call a frequency);C. Suppose that there are 60 students in this class, but the math test has passed 40 people, then the total sample is 40, it is obvious that at this time the

D. Bag Of MiceThe Dragon and the princess is arguing about-what-does on the New year's Eve. The dragon suggests flying to the mountains to watch fairies dancing in the Moonlight and while the Princess thinks they shou LD just go to bed early. They is desperate to come to a amicable agreement, so they decide to leave the to chance. they take turns drawing a mouse from a bag Which initially Contains w white and b black mice. The person was the first to draw a white mouse wins. After all mouse

Question: Give you m, t, n, representing t team, do m questions, for all teams, all do one or more questions, and at least one team has the probability of doing n questions. Practice: P [I] [j] indicates the probability that the I-th team will answer the j-th question. Dp [I] [j] [k] represents the I-th team, and the probability that the first j questions will ha

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

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

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