Problem 2, May 2003 A Poisson process [formula] having rate [lambda] has (as is well known) the following two properties: (i) [formula] and (ii) [formula]. Let [formula] and [formula] be two independent Poisson processes having rates [lambdaA] and [lambdaB], respectively. Further, let [formula]. (a) Show, by precise calculation (that is, by using o(h) notation), that N(t) satisfies the conditions (i) and (ii) with [formula]. Make use of known properties of Poisson processes to answer the following question when [formula], [formula] and [formula] are as specified above and [formula] and [formula]. (b) Determine the probabilities [formula], [formula] and [formula].