4. A pack of 52 cards contains 4 cards bearing each of the integers from 1 to 13 . A card is selected at random. The random variable \(X\) represents the number on the card.

1. Find \(\mathrm { P } ( X \leq 5 )\).
2. Name the distribution of \(X\) and find the expectation and variance of \(X\). A hand of 12 cards consists of three 2 s , four 3 s , two 4 s , two 5 s and one 6 . The random variable \(Y\) represents the number on a card chosen at random from this hand.
3. Draw up a table to show the probability distribution of \(Y\).
4. Calculate \(\operatorname { Var } ( 3 Y - 2 )\). \section*{STATISTICS 1 (A) TEST PAPER 8 Page 2}