1. The problem statement, all variables and given/known data Some supermarket gives its customers a free ”collectible” (C) for every 15 Euro's spent. There are 50 different types of Cs. Assume that each time a customer receives a C it is equally likely to be one of the 50 types. Define Ni, i = 1, 2, . . . , 49, to be the number of additional Cs that need to be obtained after i distinct types have been collected in order to obtain another distinct type, and let N denote the number of Cs collected to attain a complete set of at least one of each type. Find the pmf (probability mass function) of Ni. What famous distribution is this? (And later, after I figure this one out): Determine the expectation value of N (so not Ni) 2. Relevant equations I can't really think of any at this time, other than maybe pmf (probability mass function) for X is given by fx = P(X=x) 3. The attempt at a solution Right, so, starting with the pmf of Ni. Ni is the number of collectibles that are still required to be obtained after already getting i of them, so this is 50-i and the pmf has to do with the chance of 'being at a point Ni ', so I'd say that i = 1, or N1 = 49 is the most probably and i = 49 the least. Now, the (discrete) distributions that I know of are the point mass function, the bernoulli distribution, the binomial distribution, the geometric distribution and the Poisson distribution. I don't really see which one fits exactly, but a geometric distribution sounds alright. Could anyone provide a hint?