文档介绍：Probability Theory
Rosen 6th ed., ch. 6 (§§-)
6 Discrete Probability
An Introduction to Discrete Probability
equally likely等概率
Probability Theory
random variables 随机变量
Bays’ Theory
Expected Value and Variance
expected value 数学期望值
An Introduction to Discrete Probability
Introduction
Finite Probability
The probability binations of Events
Probabilistic Reasoning
Definition
Many experiments do not yield exactly the same results when performed repeatedly.
For example, if we toss a coin, we are not sure if we will get heads or tails.
If we toss a die, we have no way of knowing which of the six possible numbers will turn up.
Experiments of this type are called probabilistic(随机试验), in contrast to deterministic(确定) experiments, whose e is always the same.
Sample Spaces(样本空间)
A set A consisting of all the es of an experiment is called a sample space of the experiment.
With a given experiment, we can often associate more than one sample space, depending on what the observer chooses to record as an e.
Example 1
Suppose that a nickel and a quarter are tossed in the air. We describe three possible sample spaces that can be associated with this experiment.
l. if the observer decides to record as all e the number of heads observed, the sample space is A = {0, l, 2}.
2. If the observer decides to record the sequence of heads (H) and tails (T) observed, listing the condition of the nickel first and then that of the quarter, then the sample space is A= {HH, HT, TH, TT}.
3. If the observer decides to record the fact that the coins match (M) (Both heads or both tails) or do not match (N), then the sample space is A ={M, N}.
Note
In addition to describing the experiment, we must indicate exactly what the observer wishes to record.
Then the set of all es of this type e the sample space for the experiment.
A sample space may contain a finite or an infinite number of es.
In this chapter, we need only finite sample spaces.
Example 2
Determine