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# sympy.stats.smoment

All Samples(9)  |  Call(7)  |  Derive(0)  |  Import(2)
```Return the nth Standardized moment of a random expression i.e.
E( ((X - mu)/sigma(X))**n )

Examples
========
>>> from sympy.stats import skewness, Exponential, smoment
>>> from sympy import Symbol
>>> rate = Symbol('lambda', positive=True, real=True, bounded = True)
>>> Y = Exponential('Y', rate)
>>> smoment(Y, 4)(more...)
```

```        def smoment(X, n, condition=None, **kwargs):
"""
Return the nth Standardized moment of a random expression i.e.
E( ((X - mu)/sigma(X))**n )

Examples
========
>>> from sympy.stats import skewness, Exponential, smoment
>>> from sympy import Symbol
>>> rate = Symbol('lambda', positive=True, real=True, bounded = True)
>>> Y = Exponential('Y', rate)
>>> smoment(Y, 4)
9
>>> smoment(Y, 4) == smoment(3*Y, 4)
True
>>> smoment(Y, 3) == skewness(Y)
True
"""
sigma = std(X, condition, **kwargs)
return (1/sigma)**n*cmoment(X, n, condition, **kwargs)
```

```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 moment(X + Y, 4) == 12
assert cmoment(X, 2) == variance(X)
assert smoment(X*X, 2) == 1
assert smoment(X + Y, 3) == skewness(X + Y)
assert E(X, Eq(X + Y, 0)) == 0
```
```    assert variance(X) == 1/rate**2
assert skewness(X) == 2
assert skewness(X) == smoment(X, 3)
assert smoment(2*X, 4) == smoment(X, 4)
assert moment(X, 3) == 3*2*1/rate**3
```

```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 correlation(X, Y) == 0
assert correlation(X, Y) == correlation(Y, X)
assert smoment(X + Y, 3) == skewness(X + Y)
assert smoment(X, 0) == 1
assert P(X > 3) == S.Half
```