Consider a set of N jobs that are assigned to m workers for processing. Each job is randomly assigned to worker i with probability pi, for i = 1,...,m. Let N i denote the number of items assigned to...

Consider a set of N jobs that are assigned to m workers for processing. Each job is randomly assigned to worker i with probability pi, for i = 1,...,m. Let N_i
denote the number of items assigned to worker i, so that N = N₁
+ ··· + N_m. Suppose N has a Poisson distribution with mean λ. Describe the joint distribution of N₁,...,N_m.