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v0.2.20
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yh202109 committed Jul 21, 2024
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To calculate :eq:`eq_kappa2_vn2`,
we can use the MGF, :math:`\left(\sum_{j}p_je^{t_j}\right)^R`, to derive
:math:`E\left(N_{ij}^2\right) = Rp_j + R(R-1)p_j^2`,
:math:`E\left(N_{ij}^3\right) = Rp_j + 3R(R-1)p_j^2 + R(R-1)(R-2)p_j^3`, and
:math:`E\left(N_{ij}^4\right) =` (Lab Exercise; to be used in :eq:`eq_kappa2_vn3`).
:math:`E\left(N_{ij}^2\right) = Rp_j + R(R-1)p_j^2`, and
:math:`E\left(N_{ij}^3\right) = Rp_j + 3R(R-1)p_j^2 + R(R-1)(R-2)p_j^3`.

The first element of :eq:`eq_kappa2_vn2` can be calculated as [2]_ :sup:`(Eq. 12)`

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