Let x equal the number of people selected at random that you must ask

  

Let X equal the number of people selected at random that you must ask in order to find someone with the same birthday as yours. Assume that each day of the year is equally likely, and ignore February 29.
(a) What is the pmf of X?
(b) Give the value of the mean, variance, and standard deviation of X.
(c) Find P(X > 400) and P(X < 300).