first course in probability

between [0, 1], which is characterized by the values of two morphological parameters α and β.The shape of the beta distribution depends on the values of α and β. Beta distributions were used extensively in Bayesian analysis.When you set both the parameter α and β to 1 o'clock, the distribution is also known as the uniform Distribution (uniform distribution). Try different alpha and β values to see how the shape of the distribution changes.Exponential distribution (exponential distribution)An ex

movement can be converted to a value in the range of 1 to 25. Then, the () value is evenly allocated to 7, and 21 is a multiple of 7, therefore, you can perform a ing for each of the three (of course, you can also cut off the numbers after 7, but the range is too small and the efficiency is not high ), 1-3 -- "-6 --"-21 -- "7. This is equivalent probability. If a number between 22-25 is generated, two meth

What is entropy? Data Compression not only originated from the Information Theory pioneered by clude Shannon in 1940s, but also its basic principle is how small the information can be compressed. So far, it still follows a theorem in information theory, this theorem uses the term "Entropy" (Entropy) in Thermodynamic to indicate the actual amount of information to be encoded in a piece of information: Consider using a binary number consisting of 0 and 1 to encode a piece of information containing

http://www.lydsy.com/JudgeOnline/problem.php?id=2038Learned the next team, quite the orz of GodFirst of all, if you push the formula, it's easy. For query $[l,r]$$ $ans =\frac{\sum \binom{x_i}{2}}{\binom{r-l+1}{2}}$$Late repair ... Come back to mend.#include 　　 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 decide

this fairly good idea. First, there are the following conclusions: ∫n0p (B|X) DP (x) =−∫0NP (B|X) DP (x) That ∫n0p (B|X) DP (x) +∫0NP (B|X) DP (x) =0– equation (1) If according to the ∑ symbol, two constant positive probability and add how can be 0, however, when we use the ∫ symbol, we will find that this is an integral loop, the result is 0 of course is correct. Here, I mainly based on the similarity of

in the array $res[' yes ', and the remaining non-winning information is saved in $res[' no ', and finally output JSON data to the front page. foreach ($prize _arr as $key = + $val) { $arr [$val [' id ']] = $val [' V ']; } $rid = Get_rand ($arr); The prize ID is obtained according to probability $res [' yes '] = $prize _arr[$rid -1][' Prize '); //In the award unset ($prize _arr[$rid-1]);//To remove the prize from the array, The remaining awar

In the course of learning Andrew Ng's machine learning, he thought that he had the maximum likelihood estimate, the maximum posterior probability estimate, and the logistic regression, the Bayesian classification of the shutdown was very clear, but after the school pattern recognition course, my outlook on life completely overturned .... Let me give you a word. F

probability of failure q=1-p, the average number of lookups in accordance with Bernoulli's geometric distribution, E=∑KP (1-p) ^ (k-1) =1/p=n/k. G.) Assuming that there is no subscript I makes the a[i]=x. What is the average operating time of Deterministic-search? Deterministic-search the worst-case run time. Both the average and the worst lookups are n. Finally, considering a stochastic algorithm scramble-search, it first randomly transforms the in

. Calculate the probability of winning the first prize: If event a is set to {a winning prize} and Event B is set to {B won't win}, P (A) = 1 \ 3, P (B) = 2 \ 3. If the gamer chooses gate A and the goat is behind Gate B, the probability P (A branch B) = P (A branch B)/P (B) = P (a) * P (B)/P (B) = 1/3. Therefore, under this condition, the probability of win

foundation of mathematics, so that students can not be brought into the right path. At least as a class student, I feel that way. The result is a sense that the course is independent of one area and is very isolated. From some foreign books can be seen, machine learning is actually a multi-disciplinary derivative, and a lot of engineering field theory has a close connection, so that at least let us this beginner can be checked, not feel it is from th