6. Patients suffering from 'flu are treated with a drug. The number of days, \(t\), that it then takes for them to recover is modelled by the continuous random variable \(T\) with the probability density function $$\begin{array} { l l } \mathrm { f } ( t ) = \frac { 3 t ^ { 2 } ( 4 - t ) } { 64 } & 0 \leq t \leq 4
\mathrm { f } ( t ) = 0 & \text { otherwise. } \end{array}$$

1. Find the mean and standard deviation of \(T\).
2. Find the probability that a patient takes more than 3 days to recover.
3. Two patients are selected at random. Find the probability that they both recover within three days.
4. Comment on the suitability of the model.