4 Cards are drawn at random from a standard pack of 52 cards, one at a time, until one of the 4 aces is drawn. After each card is drawn, it is replaced in the pack before the next one is drawn. The random variable \(X\) represents the number of draws required to draw the first ace.

1. State fully the distribution of \(X\).
2. Find \(\mathrm { P } ( X = 10 )\).
3. Find each of the following.
   • \(\mathrm { E } ( X )\)
   • \(\operatorname { Var } ( X )\)
   A further \(k\) aces are added to the full pack and the process described above is repeated. The random variable \(Y\) represents the number of draws required to draw the first ace.
4. In this question you must show detailed reasoning. Given that \(\mathrm { P } ( Y = 2 ) = \frac { 8 } { 81 }\), find the two possible values of \(k\).