sympy.stats.Multinomial() function in Python

With the help of sympy.stats.Multinomial() method, we can create a discrete random variable with Multinomial Distribution.

A multinomial distribution is the probability distribution of the outcomes from a multinomial experiment.

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

Example #1 :

# 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)

Output :

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

Example #2 :

# 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)

Output :

/     x1  x3                      
| 24*0  *0                        
|-----------  for x1 + x2 + x3 = 4
<x1!*x2!*x3!                      
|                                 
|     0            otherwise      
\