Articles of coupon collector

A(nother) variation of the coupon collector's problem

I have come across variation of the coupon collector‘s problem that goes like this. The coupons are of $n$ different types and in infinite number (or sampled with replacement after each draw, where “draw” is defined next). At each draw, you get a variable number of coupons $X$, where $X$ is the number of consecutive […]

How many random samples needed to pick all elements of set?

This question already has an answer here: Expected time to roll all 1 through 6 on a die 2 answers

Probability of getting k different coupons in a set of S coupons, from an infinite set of N different types of coupons.

This is my slight modification to a question in the book “Introduction to Probability and Statistics for Engineers and Scientists” by Sheldon M Ross. Suppose there are N different types of coupons and suppose that each time one obtains a coupon it is equally likely to be any one of the types. Compute the probability […]

Coupon collector problem doubts

The Coupon Collector problem off Wikipedia: Suppose that there is an urn of $n$ different coupons, from which coupons are being collected, equally likely, with replacement. How many coupons do you expect you need to draw with replacement before having drawn each coupon at least once? The standard method to solve it divides the time […]

coupon collector problem with groups

I was looking at various extensions of the classical Coupon Collector problem, but couldn’t find any answers or hints for the following modification: Assume there are $n$ distinct coupons and you get them in batches of a different (random) size. That is, assume that every time you get a black box with coupons in it, […]

Coupon collector without replacement

Given a urn containing balls of $k$ distinct color such that $i$th color has $c_i$ number of balls. How many balls in expectation one needs to sample in order to to get at least one ball of each color. Problem looks very similar to coupon collector(each color being coupon) but without replacement. I am able […]

Coupon Collector Problem – expected number of draws for some coupon to be drawn twice

Suppose that there are $n$ different coupons, equally likely, from which coupons are being randomly drawn with replacement. Find the expected number of draws for some coupon to be drawn twice. I’ve attempted to solve this from the basic definition of expectation. If $N$ is a randomly variable for the number of draws for some […]

How often was the most frequent coupon chosen?

In the coupon collector‘s problem, let $T_n$ denote the time of completion for a collection of $n$ coupons. At time $T_n$, each coupon $k$ has been collected $C_k^{n}\geqslant 1$ times. Consider how often the most frequently chosen coupon, was chosen, that is, the random variable $$C^*_n=\max_{1\leqslant k\leqslant n}C_k^{n}. $$ Can one compute $E(C^*_n)$? What is […]

On average, how many friends would I need to have to have at least one friend's birthday every day?

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calculating expected number of packets.

This question already has an answer here: Expected time to roll all 1 through 6 on a die 2 answers