The number of messages that arrive at a Web site is a Poisson random variable with a mean of five messages per hour.

i) What is the probability that two messages are received in 1.0 hour?

ii) What is the probability that at least two messages are received in 0.5 hour? iii)Determine the length of the interval of time in hours such that the probability that no messages arrive during this time interval is 0.2. Use a mean of 5 messages per hour.