The learning from here is summarized as follows, the following content is from the source: http://hongyitong.github.io/2016/11/13/%E4%BA%8C%E9%A1%B9%E5%88%86%E5%B8% 83%E3%80%81%E6%B3%8A%E6%9D%BE%E5%88%86%E5%B8%83%E3%80%81%E6%AD%A3%E6%80%81% E5%88%86%E5%B8%83/
Binomial distribution: discrete probability distribution
A total of n times, the probability of occurrence of the event p, of which the probability of occurrence of x times can be calculated:
The binomial distribution can be used to collect the number of people who died of heart disease in clinical studies, the number of people who walked out of the elevator on the second floor in a crowded elevator, or the number of animals in a certain animal population that carry specific genetic traits.
All experiments are independent of each other, and each experiment has only two results: success and failure.
Expected value: μ=np
variance: σ²=np(1-p)
Poisson distribution: discrete probability distribution
Poisson distribution for a given known mean the case of a fixed time step probability of the number of events modeling. These events have nothing to do with the state in which they last occurred.
On the X axis are the discrete values of events such as 0, 1, 2, 3, 4 (and so on) (usually representing the number of occurrences of the event), and on the Y axis is the probability of occurrence of the phenomenon (usually given a known average ).
These events can be the number of accidents at the intersection, the number of birth defects, or the number of moose within one square kilometer.
official:
e is the base of the natural logarithm.
x is the number of possible occurrences of the event (a positive integer).
λ (that is, the average) is a positive number that represents the expected number of occurrences of the event in the specified interval. If the event occurs every 10 minutes within 1 hour (60 minutes), then λ is 6.
Poisson distribution is similar to binomial distribution, but Poisson distribution is to model small probability events without knowing the total number of possible occurrences of the event .
The modeling object of Poisson distribution is the number of accidents at the intersection, while the modeling object of the binomial distribution is the relative relationship between the number of accidents and the number of cars passing through the intersection.
Expected value: λ (ie, average)
Variance: the variance σ² is equal to the mean λ, that is, σ²=λ
nature:
1) The Poisson distribution is a single-parameter discrete distribution, and its parameter is λ, which represents the average number of occurrences of an event in a unit of time or space, and is also called an intensity parameter.
2) The variance σ² of the Poisson distribution is equal to the mean λ, that is, σ²=λ.
3) The Poisson distribution is asymmetric, showing a skew distribution when λ is not large. As λ increases, it quickly approaches the normal distribution. Generally speaking, when λ=20, it can be regarded as approximately normal distribution, and Poisson distribution data can be processed as normal distribution.
4) The cumulative probability of Poisson distribution is commonly used in two types: left-side cumulative and right-side cumulative. The number of events in a unit of time or space.
Normal distribution: continuous probability distribution
If there are a large number of observations, the sum of the random variables will be normally distributed.
For example, if a coin is tossed multiple times , the number of times the coin heads up in a series of coin toss will be close to a normal distribution.
Examples of normal distributions include: the height of a person in a certain country, the elevation values of a certain province, and the math test scores of 12-year-old students.
Note: The horizontal axis of the normal distribution is different, it is a continuous quantity, compared with the binomial distribution and the Poisson distribution! ! !