- The random variable \(X\) has the continuous uniform distribution over the interval [0.5, 2.5]
Talia selects a number, \(T\), at random from the distribution of \(X\)
- Find \(\mathrm { P } ( T < 1 )\)
Malik takes Talia's number, \(T\), and calculates his number, \(M\), where \(M = \frac { 1 } { T ^ { 2 } }\)
- Find the probability that both \(T\) and \(M\) are less than 2.25
Raja and Greta play a game many times.
Each time they play they use a number, \(R\), randomly selected from the distribution of \(X\)
Raja's score is \(R\)
Greta's score is \(G\), where \(G = \frac { 2 } { R ^ { 2 } }\) - Determine, giving a reason, who you would expect to have the higher total score.