1


2


3


4


5


6


7


8


9


10


11

 The distribution of the number of good elements in a sample of
 size n
 without replacement
 From a population of
 G good and
 NG = B bad elements
 Is called the
 hypergeometric distribution with parameters (n,N,G).

12


13

 Suppose each trial can result in m possible categories c_{1}, c_{2},
… , c_{m} with probabilities p_{1}, p_{2}, …
,p_{m },_{ }where p_{1}+p_{2}+…+p_{m }=
1.
 Suppose we make a sequence of n independent trials and let N_{i}
denote the number of results in the
i^{th} category c_{i}.

14

 Then for every mtuple of nonnegative integers (n_{1}, n_{2},
… , n_{m)} with n_{1}+n_{2}+…+n_{m }= n

15

 Suppose we roll a fair die 10 times and record the number of
 , , and even’s.
 Question:
 What’s the probability of seeing
 1 , 2 , 3 and 4 even numbers?

16

 Using the multinomial distribution:

17

