UCD advertise their courses to prospective students using advertisements on a social media website. The number of times these advertisements are clicked on follows a Poisson distribution with a rate of 50 per hour. (a) Calculate the probability that the advertisements are clicked on at least 3 times in a one minute period. [4] (b) Calculate the probability that more than 3 minutes pass without anybody clicking on the advertisements? [5] (c) Calculate the expected value and the variance of the waiting time (in minutes) between two consecutive clicks on the advertisements? [4] (d) The social media website charges UCD an initial 200!) for the advertisements plus 10c per click. Answer the following questions showing clearly all of your workings and reasoning. [1) How much would you expect the advertisements to cost per 24 hours? [4] (ii) Calculate the stande deviation of the cost per 24 hours. [5]