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# sympy.stats.cmoment

All Samples(10)  |  Call(8)  |  Derive(0)  |  Import(2)
```Return the nth central moment of a random expression about its mean
i.e. E((X - E(X))**n)

Examples
========

>>> from sympy.stats import Die, cmoment, variance
>>> X = Die('X', 6)
>>> cmoment(X, 3)
0(more...)
```

```        def cmoment(X, n, condition=None, **kwargs):
"""
Return the nth central moment of a random expression about its mean
i.e. E((X - E(X))**n)

Examples
========

>>> from sympy.stats import Die, cmoment, variance
>>> X = Die('X', 6)
>>> cmoment(X, 3)
0
>>> cmoment(X, 2)
35/12
>>> cmoment(X, 2) == variance(X)
True
"""
mu = expectation(X, condition, **kwargs)
return moment(X, n, mu, condition, **kwargs)
```

```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,
```
```    assert E(X + X) == 7
assert E(a*X + b) == a*E(X) + b
assert variance(X + Y) == variance(X) + variance(Y) == cmoment(X + Y, 2)
assert variance(X + X) == 4 * variance(X) == cmoment(X + X, 2)
assert cmoment(X, 0) == 1
assert cmoment(4*X, 3) == 64*cmoment(X, 3)
```

```from sympy.stats import (P, E, where, density, variance, covariance, skewness,
given, pspace, cdf, ContinuousRV, sample,
Arcsin, Benini, Beta, BetaPrime, Cauchy,
Chi, ChiSquared,
ChiNoncentral, Dagum, Erlang, Exponential,
```
```    assert correlation(X, X + Y) == correlation(X, X - Y)
assert moment(X, 2) == 1
assert cmoment(X, 3) == 0
assert moment(X + Y, 4) == 12
assert cmoment(X, 2) == variance(X)
```