In a game, the number of points scored by a player in the first round is given by the random variable \(X\) with probability distribution
\(x\)
5
6
7
8
\(\mathrm { P } ( X = x )\)
0.13
0.21
0.29
0.37
Find
\(\mathrm { E } ( X )\)
\(\operatorname { Var } ( X )\)
\(\operatorname { Var } ( 3 - 2 X )\)
The number of points scored by a player in the second round is given by the random variable \(Y\) and is independent of the number of points scored in the first round.
The random variable \(Y\) has probability function
$$\mathrm { P } ( Y = y ) = \frac { 1 } { 4 } \quad \text { for } y = 5,6,7,8$$
Write down the value of \(\mathrm { E } ( Y )\)
Find \(\mathrm { P } ( X = Y )\)
Find the probability that the number of points scored by a player in the first round is greater than the number of points scored by the player in the second round.