The Poisson distribution is a discrete probability distribution that ex- presses the probability of a given number of occurrences of an event in a fixed time interval. The probability of a number of events k is given by Ak exp(-A) P(k) = k! where A is the mean number of events. Take = 10 for this question. (a) Use for loops to find the probability that: 5 or less; 10 or less; and 15 or less events occur, expressing your answer as a decimal. (b) Use while loops to calculate the number of events we would need to see to conclude that A > 10 at the 10%, 5% and 1% confidence levels, that is, calculate the smallest integer N such P(k > N)