[] = 4.42. Let fm,B(x; n, p) be the mass function for a binomial variable with parameters n and p (the number of trials and the single trial probability of success). Let fm,p(x; k) be the mass function for a Poisson distribution with parameter k. Further suppose that the means of these two distributions are equal and that k is a constant with respect to n. Show that lim fm,B(x; n, p) = fm,P(x;k). no 4.43. Continuation Let X be the number of heads encountered when tossing 1 million fair coins. Use Stirling's approximation for the factorial to estimate the probability that X 500,000. [Stirling's Approximation: n! = n" 2an exp(-n+0/(12n)) for n >0 and 0