The number of letters arriving each day at a residential addressis assumed to be Poisson distributed with mean 1.8. The numbers ofletters arriving on different days are independent randomvariables. (i) Calculate the probability that exactly two lettersarrive at the address in one day. (ii) Calculate the probabilitythat no more than 5 letters arrive at this address in a 5 dayperiod. (iii) On a particular day, there are no letters at thisaddress. Find the probability that exactly 6 days go by before thishappens again. (iv) Use a suitable approximation to calculate theprobability that during a 30 day period, more than 65 letters arereceived at this address, with mean rate ? = 1.8 for each day
