${\tilde{t}}_n\left(x;N\right)$

${\tilde{k}}_n\left(x;p,N\right)$

${\tilde{c}}_n^{a_1}\left(x\right)$

$A$

$\frac{n}{2\left(2n-1\right)}$

$n$

$-a_1$

$B$

$x-\frac{N-1}{2}$

$x-n+1-p\left(N-2n+2\right)$

$x-n+1-a_1$

$C$

$-\frac{\left(n-1\right)\left(N^2-{\left(n-1\right)}^2\right)}{2\left(2n-1\right)}$

$-p\left(1-p\right)\left(N-n+2\right)$

$n-1$

$D$

$\sqrt{\frac{2n+1}{\left(N^2-n^2\right)\left(n+1\right)}}$

$\sqrt{\frac{n}{p\left(1-p\right)\left(N-n+1\right)}}$

$\sqrt{\frac{a_1}{n}}$

$E$

$\sqrt{\frac{2n+1}{\left(N^2-n^2\right)\left(N^2-\left(n+1\right)\right)}}\ast \sqrt{\frac{1}{2n-3}}$

$\sqrt{\frac{n}{p\left(1-p\right)\left(N-n+2\right)}}\ast \sqrt{\frac{n-1}{N-n+1}}$

$\sqrt{\frac{a_1^2}{n\left(n-1\right)}}$