Consider the lottery in which the winning ticket comprises of three digits randomly chosen from 0-9 and suppose that the order of numbers doesn't matter. Assume each week you purchase a ticket, and let X be the number of weeks till your first win.
a) Determine the distribution of X?find its parameters?
b) Determine the probability you win on the fifth week
c) How many weeks do you anticipate it will take to win.
d) Determine the probabitlity it takes more than 25 weeks to win
e) Given you haven't won by the 25th week , determine the probability that you win on 28^{th} week.