- A discrete random variable \(X\) has probability generating function given by
$$\mathrm { G } _ { X } ( t ) = \frac { 1 } { 64 } \left( a + b t ^ { 2 } \right) ^ { 2 }$$
where \(a\) and \(b\) are positive constants.
- Write down the value of \(\mathrm { P } ( X = 3 )\)
Given that \(\mathrm { P } ( X = 4 ) = \frac { 25 } { 64 }\)
- find \(\mathrm { P } ( X = 2 )\)
- find \(\mathrm { E } ( X )\)
The random variable \(Y = 3 X + 2\)
- Find the probability generating function of \(Y\)