Python中的 sympy.stats.Multinomial()函数

借助sympy.stats.Multinomial()方法，我们可以创建具有多项分布的离散随机变量。

多项分布是多项实验结果的概率分布。

Syntax: sympy.stats.Multinomial(syms, n, p)

Parameters: 
 syms: the symbol
 n: is the number of trials, a positive integer
 p: event probabilites, p>= 0 and p<= 1

Returns: a discrete random variable with Multinomial Distribution

示例 #1：

Python3

# import sympy, Multinomial, density, symbols
from sympy.stats.joint_rv_types import Multinomial
from sympy.stats import density
from sympy import symbols, pprint
  
x1, x2, x3 = symbols('x1, x2, x3', nonnegative = True, integer = True)
p1, p2, p3 = symbols('p1, p2, p3', positive = True)
  
# Using sympy.stats.Multinomial() method
M = Multinomial('M', 3, p1, p2, p3)
multiDist = density(M)(x1, x2, x3)
  
pprint(multiDist)

输出 ：

/    x1   x2   x3                      
|6*p1  *p2  *p3                        
|----------------  for x1 + x2 + x3 = 3
<  x1!*x2!*x3!                         
|                                      
|       0               otherwise      
\                                   

示例 #2：

Python3

# import sympy, Multinomial, density, symbols
from sympy.stats.joint_rv_types import Multinomial
from sympy.stats import density
from sympy import symbols, pprint
  
x1, x2, x3 = symbols('x1, x2, x3', nonnegative = True, integer = True)
  
# Using sympy.stats.Multinomial() method
M = Multinomial('M', 4, 0, 1, 0)
multiDist = density(M)(x1, x2, x3)
  
pprint(multiDist)

输出 ：

/     x1  x3                      
| 24*0  *0                        
|-----------  for x1 + x2 + x3 = 4