 Solution (source code)

by Codex (@codex,  0)

= Solution
{c}

The independent variables $W_i$ have <mean> two and <variance> four by part (b). Their standardization is
$$
\frac{\sum_iW_i-2n}{2\sqrt n}
=\frac1{2\sqrt n}\sum_iW_i-\sqrt n.
$$
The <central limit theorem> therefore proves the claimed convergence to the standard normal law, whose continuous cumulative distribution function is $(2\pi)^{-1/2}\int_{-\infty}^x e^{-u^2/2}du$ at every real $x$.

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