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P(H=1)&=&P\bigg(\bigcap_{p:{\rm prime}}(E_p\cap F_p)^c\bigg)\\
&=&\prod_{p:{\rm prime}}P<span class=
J_{1}=\left[
\begin{array}{c}
1 \\
1 \\
\end{array}
\right]
J_{3}=\left[
\begin{array}{c}
1 \\
j \\
\end{array}
\right]
\frac{\alpha x - E(X)}{\sigma(X)} = \sqrt{\frac{N^2}{N+1}}.
\left(E(X),~V(X),~{\rm median}(X)\right) = \left(\frac{(\alpha+N)}{N+1}x,~ \frac{(\alpha - 1)^2}{N+1}x^2,~ x\right).