The Super Breakfast Challenge (SBC) consists of bacon, eggs, oatmeal, orange juice, milk, and several other foods, and it costs $12.99 per person to order at a local restaurant. It is known to be very difficult to consume the entire SBC. Only 10% of people are able to eat all of the SBC. The other 90% of people will be unable to eat the whole SBC (it is too much food!).
A probability student hears about the SBC and goes to the local restaurant. He observes the number of customers, X, that attempt to eat the SBC, until the first success. So if there are 4 failures and then 1 success (i.e., the outcome is (F, F, F, F, T)), then X = 5.
a. What is the mass of X?
b. Make a plot of the probability mass function.
c. What is the CDF of X?
d. Make a plot of the CDF