The probability density function of a random variable X is f(X)(a)show that E(aX+b)=aE(X)+b(b)Var(aX+b)=a2Var(X)(c)Var(X)=E(X2)-{E(X)}2 答案 (a): Proof: E[aX+b] = Sum π(axi +b) = Sum (π (axi) + π (b)) = Sum (π axi)+ Sum ( π b) = aSum...
The exponential probability density function of random variable X is defined as f(x) = ae-"r for a 0 and x∈ [0, ∞[.Show that the mean and variance of the negative exponential variable Xare1/aand1/(a^2)respectively. 相关知识点: ...
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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...
摘要: This paper presents a new method to solve the probability distribution of a function of a random variable,which improves an existing method greatly.Utilizing several examples,we explain how to apply our method in detail.关键词: continuous random variable probability density function piecewise ...
【题目】T he probability density function of a random variable X is f(X)(a)show that E($$ E ( a X + b ) = a E ( X ) + b $$(b)$$ V a r ( a X + b ) = a ^ { 2 } V a r ( X ) $$(C)$$ V a r ( X ) = E ( X ^ { 2 } ) - \left\{ E ( X...
(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"...
Many times, in practice, however, it is not simply the measured random variable that is of interest to us. Rather, it is some function of that random variable that is of primary concern. In this chapter, we discuss three distinct techniques, each of which is valuable in different ...
If the probability of occurrence of X=xi, (I=1, 2, …, n) is P(X=xi)=pi Such that 1. P(X=xi)=pi≥0 for all i (1≤i≤n) 2. ∑i=1nP(X=xi)=∑i=1npi=1 Then the function P(X) is called the probability function of the random variable X and the set {(x1,P(X=...
之所以会出现random variable是一个function这样的迷惑性用词,是因为"random variable"这个名词的使用远早于概率论的公理化,在公理化中,人们才发现概率与分析之间的联系,才意识到函数是对随机变量更加合理的定义;但是因为公理化太晚,用词已经积重难返,才给后人学习带来这样的困惑。当然随机变量也可以用等价类的方式定...