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 \(\mu\).
5 (a) The random variable $X$ has the distribution $\operatorname { Po } ( \lambda )$.\\
(i) State the values that $X$ can take.\\
It is given that $\mathrm { P } ( X = 1 ) = 3 \times \mathrm { P } ( X = 0 )$.\\
(ii) Find $\lambda$.\\
(iii) Find $\mathrm { P } ( 4 \leqslant X \leqslant 6 )$.\\
(b) 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 $\mu$.\\
\hfill \mbox{\textit{CAIE S2 2020 Q5}}