1. 前三章知识与Probability的相似之处1.1 章节与知识节构.2.典型题型与考点..3. probability在后续章节的作用。Probability. => Cumulative Relative Frecuency.事件发生可能性的度量 : 一个数据值出现的频繁性的度量EventRandom VariableProportion (a<=X<=b)takes a value. eg. X=aor takes a range eg a<=X<=b same.P(a<=X<=b)=Distribution of Prob. vs Distr. of Data.Categorical Prob. of event A. Marginal distributionP(A)Conditional Probability: Conditional distributionP(A|B).2-way table. home awayorder food 231 134don't order food 208 80Prob. of event P(rooting for home team) = 31 / (231+206+139+80)randomly select 1 person, the probabilityof he/she rooting for home team is.....Same concept.Marginal the proportion of people not for home distribution team is ......Conditional Prob.Given that a randomly selectedperson buy food, What is the probabilitythat he is rooting for the home team.P(rooting for home team | buys food ).Conditional distributionWhat is the proportion of people rootingfor home team among the people thatbuys food.Event Independence VS Variable No Association.不论B发生与否, A的概率相同.A&B Independent P(A|B) = P(A) = P(A|BC)比例同 没关系Proportion of people rooting for homeIn people buying food.Proportion of people rooting for home teamIn people not buying food.Proportion of people rooting for home team2-variables have no association.QuantitativeRandom Variable | Variable.all have (1) Mean pop. mean sample mean.E(X) or $\mu_X$ $\mu_X$ or $\bar{X}$only in Random VariableWe call it Expected Value.用同样的符号,在SRS下,有相同数位(2) Variance. $\sum (X_i - \mu_X)^2 W_i$R.V. $\sigma_X^2$ | Variable $S_X^2$ $S_X^2$$W_i = P_i$:when all $X_i$ equally likely to happen.Pi = $1/N$$W_i = 1/(n-1)$ or $1/N$for Sample varianceStandard deviation.R.V. $\sigma_X$ | Variable $S_X$ or $S_X$Same variable transformation.Y = aX + b. a. b constant.$\\mu_Y = a\mu_X + b$. for all.$\\bar{Y} = a\bar{X} + b$.Z = aX + bY + c. a. b. c constant$\\mu_Z = a\mu_X + b\mu_Y + c$. all the same.${\bar{Z}} = a\bar{X} + b\bar{Y} + c$.Y = aX + b.Var(Y) = $a^2$ Var(X). no b.Std(Y) = $|a|$ Std(X)Z = aX + bY + cSame for Var(Z) = $a^2$ Var(X) + $b^2$ Var(Y)* X & Y independent / no relationship$\rho = 0$.Std(Z) = $\sqrt{a^2 \text{Std}(X)^2 + b^2 \text{Std}(Y)^2}$根据概率性质,做推断.Hypothesis testing. => p-value.probability.