16:47
The distribution of variables has two distinct basic characteristics: centealization and dispersion
Arithmetic mean: the sum means the number
Median: the number standing at the middle of the line
Mode: the value that has the most occurrences of the observed value Geometric:
Application scope：the geometrical mean numberis applicable to the logarithmic normal distribution of variable x, and the data of normal distribution after logarithmic transformation. Harmonic mean:
The reciprocal of the arithmetic mean of the reciprocal of the observations in the data
The important nature of arithemetic averages:
The sum of the deviations is equal to zero The square sum of the deviation is minimum
Range: the difference between the maximum value and the minimum value of a sample variable Variance:
Standard deviation:
The characteristics of standard deviation:
The size of the standard deviation, affected by multiple observations, if the observation number of large differences between the difference is also large, and vise versa is small
Coefficient of variabilit: CV=s / x × 100%
The degree of relative variability of different samples can be compared
Probabity and probility distribution
2018年3月12日 12:40
The concept:
Wheather or not something happens
Frequency: the number of occurrences of the event dicided by the total times
Probability: the frequency obtained after extensive testings, which is an approximate value. Classocalprobabilty: the probablity is calculated directy from the characteristics of the event. Geometric probablity is considered as a random experiment with an infinite number of possible basic events
The axiomatic definition of probablity:
Caculation of probability:
Plot& and events, mutex events, opposing events, independent events, complete event system
The law of probability caculation:
the addition theorem of mutex events.
定理: 若事件A与B互斥，则 P(A+B)=P(A)+P(B) 推理1 P(A1+A2+…+An)=P(A1)+P(A2)+…+P(An) 推理2 P(A)=1-P(A)
推理3 完全事件系的和事件的概率为1。
Probability distribution of discrete variables
Probability distribution of continuous type variables
The probability depend on the distribution density function
Law of large numbers: Chebyshev inequalities:
Berrnoulli's law of large numbers:
Sinchin law of large numbers:
第二节：
几种常见的理论分布：
二项分布：实验只有两个对立结果，具有重复性和独立性
二项分布的形状和参数：p值较小且n不大时，分布是偏倚的，随着n的增大，分布趋于对称；当p趋于0.5时，分布趋于对称
当n足够大时，符合泊松分布 泊松分布函数的推导：