1. The three basic random distribution uniform, exponential, normal
1. Uniform distribution
表示在相同长度间隔的分布概率是等可能的
Its probability density, mean, variance
2. Exponential distribution
事件以恒定平均速度连续且独立地发生的过程(泊松过程中的事件之间的时间的概率分布)
Its probability density, mean, variance
3. Normal distribution
常见的连续概率分布，若一个随机变量X服从一个位置参数μ，尺度参数为σ的正态分布记为
The mean is μ and the variance is σ squared
2. Mathematical characteristics of random variables
1. Expectations
Describing the magnitude of the mean value of a random variable in a random event, the mathematical expectation is defined as the sum of the probabilities of possible outcomes in an experiment multiplied by their outcomes.
用于预测一个随机事件的平均预期情况。
2. Variance
A measure of the degree of dispersion when measuring a random variable or a set of data
3. (Auto)correlation function
The autocorrelation function describes the degree of correlation between the values of the random signal X(t) at any two different moments t1, t2
4. (Auto)covariance function
It is used to describe the degree of correlation between the ups and downs (relative to the mean) of the values of X(t) at two moments, and is also called the centralized autocorrelation function.
Obviously, the characteristics described by the autocovariance function and the autocorrelation function are basically the same
5. Correlation coefficient
Eliminate the effect of the magnitude of change of two random variables, the similarity of simple response changes
3. Relationship and calculation
- The random variables X and Y are independent of each other, E(XY) = E(X)E(Y)
- D(X) = E(X^2) - [E(X)] ^2
