CH06 binomial distribution and possion distribution.ppt

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Section one binomial distribution
Section two Poisson distribution
Chapter 6 binomial distribution and
Poisson distribution
In the previous chapters,We introduced the continuous distribution. For example,t distribution and F distribution.
In this chapter, we will introduce binomial distribution and Poisson distribution.
Section one binomial distribution
The distribution of a count X depends on how the data are produces. Here is a simple mon situation.
Think of tossing a coin n times as an example of the binomial settings. Each toss gives either heads or tails. The es of essive tosses are independent . If we call heads a ess,then p is the probability of a head and remains the same as lone as we toss the same coin.
The number of heads we count is a random variable X. The distribution of X ,and more generally of the count of esses in any binomial setting ,pletely determined by the number of observations n and the essful (positive) probability p
binomial distribution definition
The distribution of the count X of esses in the binomial setting is called the binomial distribution with parameters n and p. The parameters n is the number of observations,and p is the probability of a ess on any one observation. The possible values of X are the whole numbers from 0 to n. As an abbreviation, we say that X is B(n,p).
The binomial distribution have two parameters :
Population rate :
Sample size:
We remember is as X~B(n,π)
The model is concerned with the total number of esses in n trials as a random variable, denoted by X. Its probability density function is given by
Where is binomial coefficient,
Example 6-1  10 people were tested, Population rate is p(X), X=6,7,8。