概率论与数理统计(英文).doc

Probability theory and mathematical statistics概率论与数理统计Continuous Random Variable 连续型随机变量Continuous random variables appear when we deal will quantities that are measured on a continuous scale. For instance, when we measure the speed of a car, the amount of alcohol in a persons blood, the tensile strength of new alloy.Continuous Random Variable1. Definition Definition 4.1.1A function f(x) defined on is called a probability density function （概率密度函数）if:(i) ;(ii) f(x) is intergrable on and .Definition 4.1.2 Let f(x) be a probability density function. If X is a random variable having distribution function , (4.1.1)then X is called a continuous random variable having density function f(x). In this case,. (4.1.2)2. ExampleExample 4.1.2 Find k so that the following can serve as the probability density of a continuous random variable:.3. Uniform Distribution 均匀分布If the continuous random variable x with probability density functionCalled X in the (a, b) obey uniform distribution0abxf(x)Figure 4.2.1 The uniform probability density in the interval (a, b)4. Exponential Distribution 指数分布Definition 4.5.1 A continuous variable X has an exponential distribution with parameter , if its density function is given by (4.5.1)Many random variables, such as the life of automotive parts, life of animals, time period between two calls arrives to an office, having a distribution called exponential distribution.Theorem 4.5.1 The mean and variance of a continuous random variable X having exponential distribution with parameter is given by.概率论与数理统计连续型随机变量连续型随机变量出现在我们交易量是衡量一个连续的规模。例如，我们测量汽车的速度时，一个人血液中的酒精含量，新合金的抗拉强度。连续型随机变量1.定义定义4.1.1函数f(x)定义在上，且满足下面两个条件(i);(ii)f(x)在上可积且.那么f(x)就叫概率密度函数.定义4.1.2设f（x）是一个概率密度函数。如果x是一个具有分布函数的随机变量且 (4.1.1)那么x称为一个具有连续随机变量的密度函数f（x）。在这种情况下. (4.1.2)2.范例范例4.1.2发现K，以下可以作为一个连续随机变量的概率密度：3.Uniform Distribution 均匀分布若连续型随机变量x具有概率密度函数则称x在（a,b）上服从均匀分布4.Exponential Distribution 指数分布许多随机变量，如汽车部件