Audrey, an astronomer is searching for extra-solar planets using the technique of relativistic lensing. Though there are believed to be a very large number of planets that can be found this way, actually finding one takes time and luck; and finding one planet does not help at all with finding planets of other stars in the same part of the sky. Audrey is good at it, and finds one planet at a time, on average once every three months.

a.) Find the expected value and standard deviation of the number of planets she will find in the next two years.

b.) When she finds her sixth new planet, she will be eligible for a prize. Find the expected value and standard deviation of the amount of time until she is eligible for that prize.

c.) Find the probability that she will become eligible for that prize within one year.