# Fuzzy Probability Theory---(3)Discrete Random Variables

We start with the fuzzy binomial. Then we discuss the fuzzy Poisson probability mass function.

### Fuzzy Binomial

Let $E$ be a non-empty, proper subset of $X=\{x_1,x_2,x_3,...,x_n\}$. Let $P(E)=p$ so that $P(E^{‘})=1-p$ where $p\in (0,1)$. Suppose we have $m$ independent repetitions of this experiment. If $P(r)$ is the probability of $r$ successes in the $m$ experiments, then $$P(r)=C^{r}_{m}p^{r}(1-p)^{m-r}$$ for $r=0,1,...,m$ gives the binomial distribution.

We substitute

## 3.Discrete Random Variables and Probability Distributions

1. Random Variables Random variables  variable: because different numerical values are possible; random: because the observed value depends on which of the possible experimental outcomes results. For a given sample space δ of some experiment, a rando

## Introduction to Probability (5) Discrete random variable 1.Basic concept 随机变量的定义:随机变量是指针对实验结果的函数. 随机变量的函数可以生成另外一个随机变量 离散型随机变量的定义: 离散型随机变量是指有有限个取值的实验结果的实值函数.每个离散型随机变量有PMF给出每个随机变量取值的概率. 2.PMF(probability mass function) 如何获得PMF? 将随机变量X取值x的所有概率相加,得到Px(x). 伯努利分布:对于一件事情发生与否的概率分布,发生的概率为P,例如掷一枚硬币,head的概率为P,那么PMF为:

## CCJ PRML Study Note - Chapter 1.2 : Probability Theory

Chapter 1.2 : Probability Theory Chapter 1.2 : Probability Theory Christopher M. Bishop, PRML, Chapter 1 Introdcution Chapter 1.2 : Probability Theory 1. Uncertainty 2. Example discussed through this chapter 3. Basic Terminology 3.1 Probability densi

## 一起啃PRML - 1.2 Probability Theory @copyright 转载请注明出处 http://www.cnblogs.com/chxer/ A key concept in the field of pattern recognition is that of uncertainty. 可以看出概率论在模式识别显然是非常重要的一大块. 读其他书的时候在概率这方面就也很纠结过. 我们也还是通过一个例子来理解一下Probability Theory里面一些重要的概念. Imagine we have two boxes, one red a

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