Independence in Coupon Collecting Problem If $T_i$ is the number of cards that we draw from a deck before seeing the $(i+1)$th new card (after seeing the ith new card), how can I show that Then $T_i$ and $T_j$ are independent (for i≠j)? I know the definition of independence, but I don't know how to get a workable second definition to compare to $P(T_j)P(T_i)$.
In both cases you have a geometric distribution.  If there are $n$ cards in total, the chance of success after having seen $i$ cards is $\frac {n-i}n$.  This clearly is independent of $j$
In both cases you have a geometric distribution.  If there are $n$ cards in total, the chance of success after having seen $i$ cards is $\frac {n-i}n$.  This clearly is independent of $j$