Basic Statistics

Basic Statistics

Expected Value

E[X]=∑P(X=xi)xi

Variance

σ2=E[(X-μ)2]

σ2=E[X2]-(E[X])2

Covariance

Cov[X,Y]=E[(X-E[X])(Y-E[Y])]

Cov[X,Y]=E[XY]-E[X]E[Y]

Correlation

Sums of Random Variables(https://www.daowen.com)

●　If X and Y are any random variables:E(X+Y)=E(X)+E(Y)

●　If X and Y are independent:

Var(X+Y)=Var(X)+Var(Y)

●　If X and Y are not independent:

Var(X+Y)=Var(X)+Var(Y)+2Cov(X,Y)

Skewness& kurtosis

Positive skewness:Mode＜Median＜Mean

Negative skewness:Mode＞Median＞Mean

Excess kurtosis=sample kurtosis-3