- The independent random variables \(W\) and \(X\) have the following distributions.
$$W \sim \operatorname { Po } ( 4 ) \quad X \sim \mathrm {~B} ( 3,0.8 )$$
- Write down the value of the variance of \(W\)
- Determine the mode of \(X\)
Show your working clearly.
One observation from each distribution is recorded as \(W _ { 1 }\) and \(X _ { 1 }\) respectively.
- Find \(\mathrm { P } \left( W _ { 1 } = 2 \right.\) and \(\left. X _ { 1 } = 2 \right)\)
- Find \(\mathrm { P } \left( X _ { 1 } < W _ { 1 } \right)\)