A random variable \(X\) has the distribution \(\mathrm { B } ( 2540,0.001 )\). Use the Poisson approximation to the binomial distribution to find \(\mathrm { P } ( X > 1 )\).
Explain why the Poisson approximation is appropriate in this case.
Two independent random variables, \(S\) and \(T\), have distributions \(\operatorname { Po } ( 2.1 )\) and \(\operatorname { Po } ( 3.5 )\) respectively. Find the mean and standard deviation of \(S + T\).