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# sympy.stats.moment

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```Return the nth moment of a random expression about c i.e. E((X-c)**n)
Default value of c is 0.

Examples
========

>>> from sympy.stats import Die, moment, E
>>> X = Die('X', 6)
>>> moment(X, 1, 6)
-5/2(more...)
```

```        def moment(X, n, c=0, condition=None, **kwargs):
"""
Return the nth moment of a random expression about c i.e. E((X-c)**n)
Default value of c is 0.

Examples
========

>>> from sympy.stats import Die, moment, E
>>> X = Die('X', 6)
>>> moment(X, 1, 6)
-5/2
>>> moment(X, 2)
91/6
>>> moment(X, 1) == E(X)
True
"""
return expectation((X - c)**n, 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 P(Eq(X, Y)) == P(Eq(X, 1))

assert E(X, X > 3) == 5 == moment(X, 1, 0, X > 3)
assert E(X, Y > 3) == E(X) == moment(X, 1, 0, Y > 3)
assert E(X + Y, Eq(X, Y)) == E(2*X)
assert moment(X, 0) == 1
assert moment(5*X, 2) == 25*moment(X, 2)
```

```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, Y) == 0
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 skewness(X) == smoment(X, 3)
assert smoment(2*X, 4) == smoment(X, 4)
assert moment(X, 3) == 3*2*1/rate**3
assert P(X > 0) == S(1)
assert P(X > 1) == exp(-rate)
```
```            (0, True))
# assert simplify(variance(X)) == k*theta**2  # handled numerically below
assert E(X) == moment(X, 1)

k, theta = symbols('k theta', real=True, bounded=True, positive=True)
```