本章主要介绍随机变量,离散型随机变量(discrete random variables),期望(expected value),方差(variance),Bernoulli试验和二项分布(The Bernoulli and Binomial random variables),Poisson分布(The Poisson Random Variable),累积分布函数(Cumulate Distribute Variance Function) 后面重要名词均以英语展示 Random Variable 定义...
= aSum (π xi)+ bSum ( π), Sum( π) = 1,所以 Sumaxi = aSxi = aE[X] + b(b) ProofVar(X) = E([X-E(X)]2= E(X2)-2XE(X) + E(X)2, x=E(x)= E(X2) -2E(X)E(X) + E(X)2= E(X2)-E(X)2(c)Proof: Var[aX+b]= E([(aX + b)- E(aX + b)]2)=...
(i)Show that the probability generating function of a random variable with the distribution B(n, p)is(1-p+pt)^n . [3] 相关知识点: 试题来源: 解析 r=0 ∑(pt)""C,(1-p)"-" r=0 =(1-p+pt)^n AGUse∑t'P(R=r) and binomial probabilities Indicate correct final term Collect p"...
5) expect,expectation(of a random variable or of a probability distribution) 期望(随机变量或概率分布的)6) double random parametric space 重随机参变概率空间补充资料:离散变量与连续变量 分子式:CAS号:性质: 符号x如果能够表示对象集合S中的任意元素,就是变量。如果变量的域(即对象的集合S)是离散的,...
当(\Omega^\prime, \mathcal{B}^\prime)=(\mathbb{R},\mathcal{B}(\mathbb{R}))时,这个可测映射X称为一个随机变量(random variable)。 从可测映射的定义,我们看到它其实是用原像或者说逆映射来定义的。一个有意思的问题是:为什么我们不能直接用X(\mathcal{B})\subseteq \mathcal{B}^\prime来定义...
aThe probability distribution of a discrete random variable is a table, graph, or formula that gives the probability associated with each possible value that the variable can assume 一个分离随机变量的概率分布是给可能性与每可能的价值相关可变物可能假设的桌、图表或者惯例[translate]...
结果1 题目 4.Expected values of random variables The table below shows the probability distribution of a random variable Y.160.2170.3180.2190.3What is the expected value of Y?Write your answer as a decimal. 相关知识点: 试题来源: 解析 17.6 反馈 收藏 ...
Let X be a random variable with a probability density function f(r) given by f(z)=\(e-z0.0y+z_0=1. fo 0x∞for ≤ 0.Answer the following questions.(1)Find the mean and the variance of X.(2)Find the moment generating function M(t)=E(e^(tΔ)j for a real variable t less ...
Aboubaker Gherbi, Mourad Belgasmia Explore book 2.1 Probability density function As a random process is a succession of values that are very close to each other, it is natural to characterize it in the same manner of a random variable (see detail of random variables (Denol, 2002; Newland...
IV. FUNCTIONS OF A RANDOM VARIABLE 4.1 TRANSFORMATIONS OF RANDOM VARIABLES 4.2 MATHEMATICAL EXPECTATION 4.2.1 The Expectation of Y = g(X) 4.2.2 The Linearity of Expectation 4.2.3 Conditional Expectation 4.3 MOMENTS 4.3.1 Variance 4.3.2 General Moments 4.3.3 The Chebyshev Inequality...