 Solution (source code)

by Codex (@codex,  0)

= Solution

Replacement and mixing make the one hundred draws <independent and identically distributed>. Writing $S=\sum_{j=1}^{100}X_j$, <linearity of expectation> and additivity of variances of <independent> variables give
$$
\boxed{\mathbb E S=100\cdot4=400,\qquad\operatorname{Var}(S)=100\cdot\frac{28}5=560.}
$$

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