The discrete random variable \(X\) has the following probability distribution
\(x\)
0
2
3
6
\(\mathrm { P } ( X = x )\)
\(p\)
0.25
\(q\)
0.4
Find in terms of \(q\)
\(\mathrm { E } ( X )\)
\(\mathrm { E } \left( X ^ { 2 } \right)\)
Given that \(\operatorname { Var } ( X ) = 3.66\)
show that \(q = 0.3\)
In a game, the score is given by the discrete random variable \(X\)
Given that games are independent,
calculate the probability that after the 4th game has been played, the total score is exactly 20
A round consists of 4 games plus 2 bonus games. The bonus games are only played if after the 4th game has been played the total score is exactly 20
A prize of \(\pounds 10\) is awarded if 6 games are played in a round and the total score for the round is at least 27
Bobby plays 3 rounds.
Find the probability that Bobby wins at least \(\pounds 10\)