The random variable \(X\) has the distribution \(\operatorname { Po } ( \lambda )\).
State the values that \(X\) can take.
It is given that \(\mathrm { P } ( X = 1 ) = 3 \times \mathrm { P } ( X = 0 )\).
Find \(\lambda\).
Find \(\mathrm { P } ( 4 \leqslant X \leqslant 6 )\).
The random variable \(Y\) has the distribution \(\operatorname { Po } ( \mu )\) where \(\mu\) is large. Using a suitable approximating distribution, it is found that \(\mathrm { P } ( Y < 46 ) = 0.0668\), correct to 4 decimal places.
Find \(\mu\).