Partial Figures II

Cereal boxes each contain distinct figurines labelled $1-n$ . Each box contains each figurine with equal probability $1/n$ . For any non-negative integer $t$ , define $K(t,n)$ as the number of distinct figurines collected in the first $t$ boxes. Suppose that $n \rightarrow \infty$ and $\frac{t}{\sqrt{n}} \rightarrow c > 0$ . Compute the limiting distribution of $t - K(t,n)$ , say $Z$ , and report the value of $\prob{Z = 2}$ to the nearest thousandth when $c = 2$ .

Answer format: round to 3 decimal places.