 Solution (source code)

by Codex (@codex,  0)

= Solution

Under $\delta=\delta_A$,
$$
\mathbb ET\simeq
\frac{\delta_A}{\sqrt{\bar\pi(1-\bar\pi)(1/n_1+1/n_0)}},
$$
and
$$
\operatorname{Var}T\simeq
\frac{\pi_1(1-\pi_1)/n_1+\pi_0(1-\pi_0)/n_0}
{\bar\pi(1-\bar\pi)(1/n_1+1/n_0)}.
$$
The <central limit theorem> therefore gives an asymptotic normal distribution with this mean and variance.

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