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# sympy.stats.DiscreteUniform

All Samples(3)  |  Call(2)  |  Derive(0)  |  Import(1)
```Create a Finite Random Variable representing a uniform distribution over
the input set.

Returns a RandomSymbol.

Examples
========

>>> from sympy.stats import DiscreteUniform, density
>>> from sympy import symbols(more...)
```

```        def DiscreteUniform(name, items):
"""
Create a Finite Random Variable representing a uniform distribution over
the input set.

Returns a RandomSymbol.

Examples
========

>>> from sympy.stats import DiscreteUniform, density
>>> from sympy import symbols

>>> X = DiscreteUniform('X', symbols('a b c')) # equally likely over a, b, c
>>> density(X).dict
{a: 1/3, b: 1/3, c: 1/3}

>>> Y = DiscreteUniform('Y', list(range(5))) # distribution over a range
>>> density(Y).dict
{0: 1/5, 1: 1/5, 2: 1/5, 3: 1/5, 4: 1/5}

"""
return rv(name, DiscreteUniformDistribution, *items)
```

```from sympy import (EmptySet, FiniteSet, S, Symbol, Interval, exp, erf, sqrt,
symbols, simplify, Eq, cos, And, Tuple, Or, Dict, sympify, binomial,
factor)
from sympy.stats import (DiscreteUniform, Die, Bernoulli, Coin, Binomial,
Hypergeometric, P, E, variance, covariance, skewness, sample, density,
```
```def test_discreteuniform():
# Symbolic
a, b, c = symbols('a b c')
X = DiscreteUniform('X', [a, b, c])

assert E(X) == (a + b + c)/3
assert simplify(variance(X)
- ((a**2 + b**2 + c**2)/3 - (a/3 + b/3 + c/3)**2)) == 0
assert P(Eq(X, a)) == P(Eq(X, b)) == P(Eq(X, c)) == S('1/3')
```