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...
Further, the chapter describes some well-known probability inequalities that enable us to derive bounds on probabilities of random variables when only their mean and variance are known. Finally, it explains multivariate normal distribution. conditional probability; continuous random variable; discrete ...
1.Random Variable 定义 2. Continuous rv and discrete rv 3.对于离散型 pmf 因为rv被看作是一种定义在样本空间上的实值函数 我们找一种办法来描述这个函数 性质如下 4.对于连续型 pdf 性质如下 两个函数都有相类似的性质 都得要求是 non-negative,且和(积分)为1 5. 离散型rv和连续型rv的Cumulative Dis...
3.4 CONDITIONAL DISTRIBUTION FUNCTIONS AND DENSITY FUNCTIONS 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 ...
1. Continuous Random Variables and Probability Density Functions A random variable whose set of possible values is an entire interval of numbers is not discrete. Continuous Random Variables A random variable X is said to be continuous if its set of possible values is an entire interval of numbers...
Further, the chapter describes some well-known probability inequalities that enable us to derive bounds on probabilities of random variables when only their mean and variance are known. Finally, it explains multivariate normal distribution. conditional probability; continuous random variable; discrete ...
and 5 are non-defective. If a school makes a random purchase of 2 of these computers, find the probability distribution of the number of defectives. Solution: We need to find the probability distribution of the random variable: X = the number of defective computers purchased. Experiment: ...
Probability Distribution A probability distribution is an assignment of probabilities to the specific values of a random variable, or to a range of values of the random variable. Discrete: probability assigned to each value of the random variable (and the sum = 1) ...
Conditioning One Random Variable on Another X,Y是连续随机变量。其联合分布为:fX,Y,X相对于Y的条件概率为: 条件概率也满足normalization的公式: 期望和条件概率的期望例如以下: Inference and the Continuous Bayes’ Rule 对于连续的随机变量,也存在贝叶斯准则: ...
Probability Theory and Random VariablesThis chapter collects the basic terms from probability theory and statistics. It motivates the axiomatic approach for the concept of probability, introduces the concept of a random variable,...doi:10.1007/978-3-319-11550-4_2Wolfgang Förstner...