- The discrete random variable \(X\) has probability generating function
$$\mathrm { G } _ { X } ( t ) = \frac { t ^ { 2 } } { ( 3 - 2 t ) ^ { 2 } }$$
- Specify the distribution of \(X\)
A fair die is rolled repeatedly.
- Describe an outcome that could be modelled by the random variable \(X\)
- Use calculus and \(\mathrm { G } _ { X } ( t )\) to find
- \(\mathrm { E } ( X )\)
- \(\operatorname { Var } ( X )\)
The discrete random variable \(Y\) has probability generating function
$$\mathrm { G } _ { Y } ( t ) = \frac { t ^ { 10 } } { \left( 3 - 2 t ^ { 3 } \right) ^ { 2 } }$$
- Find the exact value of \(\mathrm { P } ( Y = 19 )\)