Probability & Random Variable Distribution. Relative Frequencies / cumulative relative frequencies & Sample/population data distribution 数据 Data <=> 随机变量 R.V. 互为因果. Relative Frequency <=> PDF. P(X=a) Cumulative relative frequency <=> CDF P(X<=a). 2-Way table for 2 variables relative frequency / prob. table. Prob. of a Event <=> Marginal distribution. Conditional Prob. of a Event <=> Conditional distribution. Transformation of variable. 1) shape of new variable. 2) center (mean) of new variable 3) spread (std) of new variable. a new variable Y. Y=ax+b E(Y) = aE(X) + b. Std(Y) = |a|Std(X) shape Y same skewness if a>0 Same modalities. unimodal/bimodal. a new variable Z for 2 old variables X,Y. Z = ax + by + c. shape of Z unknown except for X&Y both normal. => Z is normal E(Z) = aE(X) + bE(Y) + C Std(Z) = √a^2 Std(X)^2 + b^2 Std(Y)^2 * when X & Y independent