离散型随机变量

中文字数:7206,中文页数:16  英文字数:4818页数:18

DEFINITIONS
Chapter 1 defines a probability model. It begins with a physical model of an experiment. An experiment consists of a procedure and observations. The set of all possible observations, S , is the sample space of the experiment. S is the beginning of the mathematical probability model. In addition to S, the mathematical model includes a rule for assigning numbers between 0 and 1 to subsets A of S. Thus for every , the model gives us a probability P[A], where .
 In this chapter and for most of the remainder of the couse, we will examine probability models in which a number is assigned to each outcome in the sample space. When we observe one of these numbers, we refer to the observation as a random variable. In our notation,the name of a random variable is always a capital letter, for example, X . The set of possible values of X is the range of X. Since we often consider more than one random variable at a time, we denote the range a random variable by the letter S with a subscript which is the name of the random variable. Thus  is the range of random variable X and  is the range of random variable Y and so forth. We use  to denote the range of X since the set of all possible values of X is analogous to S, the set of all possible outcomes of an experiment.
 A probability model always begins with an experiment. Each random variable is related directly to this experiment. There are three types of relationships.
 

2.1 定义
 第一章定义了一种概率模型。它始于一个物理模型试验。实验包括程序和观测。所有可能的观测值,S，是实验的样本空间。S是数学可能性模型的起点。 除S之外，数学模型包括一个在0和1之间S的子集A分配数字的规则。因此每个,当时,给了我们一个概率P[j]。
 在这一章,对于大多数剩下的课程中,我们将研究在每个样本空间中取得了一系列概率模型的结果。当我们看到这些数字,我们指的是观察一个随机变量。在我们的记法，一个随机变量的名字总是一个大写字母，例如， X。 全部X的可能的取值是X的范围。 当我们经常在一次实验中考虑更多的随机变量，我们由随机变量的名字X作为S的下标,表示一个随机变量的取值范围。因而,是随机变量X的范围和是随机变量Y的范围等等。 我们使用表示X的范围，因为X的所有可能的取值是取决于S，实验的所有可能的结果。
 一种概率模型常常始于一个实验。每一个随机变量是直接关系到试验。总共有三种类型的关系。

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