1 A learner driver keeps taking the driving test until she passes. The number of attempts taken, up to and including the pass, is denoted by \(X\).
- State two assumptions needed for \(X\) to be well modelled by a geometric distribution.
Assume now that \(X \sim \operatorname { Geo } ( 0.4 )\).
- Find \(\mathrm { P } ( X < 6 )\).
- Find \(\mathrm { E } ( X )\).
- Find \(\operatorname { Var } ( X )\).