The random variable \(X\) has the distribution \(\operatorname { Po } ( 2.3 )\).
Find \(\mathrm { P } ( 2 \leqslant X \leqslant 4 )\).
Find the probability that the sum of two independent values of \(X\) is greater than 2 .
The random variable \(S\) is the sum of 50 independent values of \(X\). Use a suitable approximating distribution to find \(\mathrm { P } ( S \leqslant 110 )\).
The random variable \(Y\) has the distribution \(\mathrm { Po } ( \lambda )\). Given that \(\mathrm { P } ( Y = 3 ) = \mathrm { P } ( Y = 5 )\), find \(\lambda\).