Bernoulli Random Variable 指的是取值只有0和1的随机变量 两种类型的随机变量 Discrete :能取到可数个取值的随机变量叫做离散随机变量 Continuous : 1.他的取值包括在数轴上一个区间内的所有数或者多个不相交区间的并的所有数 2.任何可能取值的概率都不是正的 Probability Distributions for Discrete Random Variables(...
This introductory chapter of the book presents the gist of probability theory. It first discusses the probability space, and the conditional probability and independence. The chapter then introduces the concept of the random variable with an example. A random variable that takes integer values is ...
A random variable X is said to be continuous if its set of possible values is an entire interval of numbers -- that is, if for some A<B, any number x between A and B is possible. Probability Distribution of Continuous Variables Let X be a continuous rv. Then aprobability distributionor...
(1) Discrete random variable (2) Continuous random variable. Discrete Random Variable Adiscrete random variable is one in which the set of all possible values is at most a finite or a countably infinite number. (Countably infinite means that all possible value of the random variable can be...
Find the CDF of the random variable X with the probability function: Example: Find the CDF of the random variable X with the probability function: X 1 2 F(x) Solution: F(x)=P(Xx) for <x< For x<0: F(x)=0 For 0x<1: F(x)=P(X=0)= For 1x<2: F...
Random Variables (Single Variable)DefinitionA random variable is some function that assigns a real number X(s) to each possible outcome s \in S, where S is the sample space for an experiment.Random …
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) ...
DefinitionA random variable iscontinuous(or absolutely continuous) if and only if its support is not countable; there is a function , called the probability density function (or pdf or density function) of , such that, for any interval
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: ...
3.2.2 Extended Notion of a Probability Density Function 3.3 CLASSICAL DISTRIBUTIONS 3.3.1 Discrete Distributions 3.3.2 Continuous Distributions 3.4 CONDITIONAL DISTRIBUTION FUNCTIONS AND DENSITY FUNCTIONS IV. FUNCTIONS OF A RANDOM VARIABLE 4.1 TRANSFORMATIONS OF RANDOM VARIABLES ...