3. When Rohit plays a game, the number of points he receives is given by the discrete random variable \(X\) with the following probability distribution.
| \(x\) | 0 | 1 | 2 | 3 |
| \(\mathrm { P } ( X = x )\) | 0.4 | 0.3 | 0.2 | 0.1 |
- Find \(\mathrm { E } ( X )\).
- Find \(\mathrm { F } ( 1.5 )\).
- Show that \(\operatorname { Var } ( X ) = 1\)
- Find \(\operatorname { Var } ( 5 - 3 X )\).
Rohit can win a prize if the total number of points he has scored after 5 games is at least 10. After 3 games he has a total of 6 points. You may assume that games are independent.
- Find the probability that Rohit wins the prize.