管理统计学之随机变量教材课件.ppt

管理统计学第五章2：随机变量及其重要的离散概率分布Random Variables and Some Important Discrete Probability Distributions 学习目标 Learning Objectives1. 计算离散随机变量的期望值和方差 Compute the Expected Value Variance of Discrete Random Variables2. 描述二项、泊松和超几何概率分布 Describe the Binomial, Poisson, Hypergeometric Probability Distributions3. 介绍两个随机变量的协方差与和的思想Introduce the Ideas of Covariance and Sum of Two Random Variables Random Variables(R.V.)—using variables denoting events Properties: ①choosing value randomly,the probability of choosing value is definite. ②being divided into continuous variables and discrete variables ③often being denoted by capital letter X,Y….Random Variables and Their Distributions The distribution of discrete r.v. X x1 x2 …... xn Pi P1 P2 …. Pn Writing like P(X=xi)= formula is also ok. For example: P(X=i)=The Distribution of R.V.(n may be∞, Pi≥0)PXxxx(|)!?????e- The distribution of continuous r.v.①The distribution function: F（x）=P（Xx） It can describe discrete r.v. too. 0≤F（x）≤1， F（x）is nondecreasing as x increases↗ F（∞）=?，F（-∞）=?②The distribution density function: f（x） f（x）≥0， F（x）= , F′（x）=f（x）.The Distribution of R.V.=1. ③The geometrical meaning of density f(x)④If X is a continuous r.v., then P(X=a)=0, so F(x)=P(Xx)=P(X≤x)⑤How to compute probability? P(X≤a)=F(a), P(Xa)=1-F(a) P(aXb)=F(b)-F(a) For example: Which of the following formulas are impossible? P(X=6)=0.8 P(X=10)=1.3 F(3.2)=1.6 f(1.5)=0.8 F1(3)=0.5 F1(4)=0.4 f2(3)=1.6 f2(4)=1.0Random Variables and Their Distributions 离散随机变量 Discrete Random Variable1. 用数