Q3. Birds land on a bird table, on average, once every 15 minutes. If food has just been left, then the average time between birds landing changes to once every 5 minutes.

a) Suppose that the gardener has just put out food for the birds. What is the probability that there will be 10 birds visiting the table within the first half hour? [6]

b) What is the probability that there will be less than three minutes between one bird visiting and the next? [6]

c) If food has not been put out for a while, what is the probability that at least two birds will visit within five minutes? [6]

d) The averages quoted here refer to day-time visits only. A bird-watcher notes that at night, the probability of waiting one hour between one bird visiting and the next is 0.1. What is the average number of visits per hour? [Hint: you need to compute the parameter "lambda"] [7]