= Solution
Let $X_i$ be <independent and identically distributed random variables> with mean $0$ and <variance> $\sigma^2\in(0,\infty)$, and put $S_0=0$, $S_k=\sum_{i=1}^kX_i$. Define the polygonal interpolation
$$
W_n(s)=\frac{S_{\lfloor ns\rfloor}+(ns-\lfloor ns\rfloor)X_{\lfloor ns\rfloor+1}}{\sigma\sqrt n}\qquad(0\leq s\leq1),
$$
with the endpoint $W_n(1)=S_n/(\sigma\sqrt n)$. The <Donsker invariance principle> states
$$
\boxed{W_n\ \Rightarrow\ B\quad\text{in }C([0,1])\text{ with the uniform topology},}
$$
where $B$ is standard one-dimensional <Brownian motion> and the arrow denotes <weak convergence of probability measures> on this path space. Equivalently, the step interpolation converges in the <Skorokhod space> with its $J_1$ topology. The continuous interpolation version is sufficient for the maximum in part (c).
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