- The discrete random variables \(W , X\) and \(Y\) are distributed as follows
$$W \sim \mathrm {~B} ( 10,0.4 ) \quad X \sim \operatorname { Po } ( 4 ) \quad Y \sim \operatorname { Po } ( 3 )$$
- Explain whether or not \(\mathrm { Po } ( 4 )\) would be a good approximation to \(\mathrm { B } ( 10,0.4 )\)
- State the assumption required for \(X + Y\) to be distributed as \(\operatorname { Po } ( 7 )\)
Given the assumption in part (b) holds,
- find \(\mathrm { P } ( X + Y < \operatorname { Var } ( W ) )\)