5. The waiting time, \(T\) minutes, of a customer to be served in a local post office has probability density function
$$\mathrm { f } ( t ) = \begin{cases} \frac { 1 } { 50 } ( 18 - 2 t ) & 0 \leqslant t \leqslant 3
\frac { 1 } { 20 } & 3 < t \leqslant 5
0 & \text { otherwise } \end{cases}$$
Given that the mean number of minutes a customer waits to be served is 1.66
- use algebraic integration to find \(\operatorname { Var } ( T )\), giving your answer to 3 significant figures.
- Find the cumulative distribution function \(\mathrm { F } ( t )\) for all values of \(t\).
- Calculate the probability that a randomly chosen customer's waiting time will be more than 2 minutes.
- Calculate \(\mathrm { P } ( [ \mathrm { E } ( T ) - 2 ] < T < [ \mathrm { E } ( T ) + 2 ] )\)
| VIXV SIHIANI III IM IONOO | VIAV SIHI NI JYHAM ION OO | VI4V SIHI NI JLIYM ION OO |