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SOLUTIONS
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Statistical Moments and Generating Functions
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Moment
BUILT-IN MATHEMATICA SYMBOL
Moment
Moment[list, r]
gives the r
sample moment of the elements in list.
Moment[dist, r]
gives the r
moment of the symbolic distribution dist.
Moment[..., {r1, r2, ...}]
gives the ![]()
multivariate moment.
Moment[r]
represents the r
formal moment.
DetailsDetails
- Moment is also known as a raw moment.
- Moment handles both numerical and symbolic data.
- For the list
, the r
moment is given by
. - Moment[{{x1, y1, ...}, ..., {xn, yn, ...}}, {rx, ry, ...}] gives
. - Moment works with SparseArray objects.
- For a symbolic distribution dist, the r
moment is given by Expectation[xr, x
dist]. - For a multivariate symbolic distribution dist, the

moment is given by Expectation[x1r1x2r2..., {x1, x2, ...}
dist]. - Moment[r] can be used in functions such as MomentConvert and MomentEvaluate, etc.
ExamplesExamplesopen allclose all
Basic Examples (5)Basic Examples (5)
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Compute the second moment
of a continuous univariate distribution:
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The moment
for a discrete univariate distribution:
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The moment
for a multivariate distribution:
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Convert a formal moment to central moments:
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Evaluate for a particular distribution:
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