# Questions tagged [coupon-collector-problem]

In probability, the coupon collector's problem models "collect all the coupons and win" contests. In its simplest form, suppose n distinct types of coupon are equally likely to occur: what is the expected number of coupons we must draw to collect at least one of each type?

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### Coupon collector inside the coupon collector

Consider the coupon collector problem, in which $n$ coupons must be collected and one coupon appears randomly daily. It is well-known that it takes an average of $n H_n$ days to collect all coupons, ...
10 views

### Estimating a subpopulation's size based on distribution

Say I have population $n_1{}$, where each individual samples is unique and contains multiple traits. A subset of population$n_1{}$ forms a population that I'm interested in, called $n_2{}$. Each ...
34 views

### Hypothetical roulette problem [duplicate]

If you have a roulette table that has 7,000,000 places and you have 10 balls (and only one ball can fit onto each number at every roll), how many rolls would it likely take for a ball to land on every ...
67 views

### Total distribution of m geometric distributions [duplicate]

Suppose that you made a webpage and you are collecting the statistics from the visitors. There are m types of visitors (students, company recruiters, etc.). Each visit is equally likely to be any of ...
431 views

### Multinomial distribution conditional on number of distinct items

I want to sample from the integers $\{1, \dots, k\}$ with probabilities $\{ p_i \}_{i=1}^k$, with replacement, until I see $m$ distinct elements (call that $n$ times). You can view the distribution I ...
7k views

### How many stickers do I need to complete my FIFA Panini album?

I'm playing the FIFA Panini Online Sticker Album, which is an Internet adaption of the classic Panini albums that are usually published for the soccer world cup, European championship, and possibly ...
1 vote
144 views

### How many samples are needed to observe every subject?

I have this problem. I have to analyze 13 chemical substances (n=13) in more than one analysis cycle. In each cycle of analysis, 8 substances are randomly chosen (m=8) to be analyzed. I would like to ...
203 views

### Expected Unique Toys [duplicate]

Suppose there are n types of toys, which you are collecting one by one. Each time you collect a toy, it is equally likely to be any of the n types. What is the expected number of distinct toy types ...
396 views

### Intuition about the coupon collector problem approaching a Gumbel distribution

The coupon collector's problem Let there be $n$ different types of coupons and we try to collect all of the types. We do this by independent random draws of coupons in which each type of coupon has an ...
25 views

### How can I find the expectation value to this problem?

At a wedding reception on an evening the representative of the host is taking it as an occasion to exercise and explain a classical analytic problem. specifically, he insists that he would start ...
1 vote
83 views

### Calculate probability

Assume that a remailer reorders messages. It has a pool of n-1 messages at all times. When the nth message arrives, one of the n messages is selected at random and forwarded. An attacker fools the ...
1 vote
73 views

### Probability of all points has been sampled after M trials

If I have a sequential dataset of size 10,000 (e.g. timeseries) and sampling randomly a batch size of 100 random values, each point of the 100 is sampled with the next 5 points after it. so basically ...
208 views

### How many unique values can you expect after throwing a die with k sides?

I ended up asking here. My problem might be familiar with the coupon collector's problem and related to this post Probability of throwing n different numbers in m throws of a die but it does not solve ...
1 vote
47 views

### How many random draws needed to sample a uniform space?

I am looking for a way to estimate how many random draws took place to produce a produce a known number of unique results. I'm sampling a uniform distribution. For example, if there were a lottery ...
242 views

### Combinatorics - calculating probability of choosing n people from m groups of k people

I am trying to calculate and understand the following question: I have 10 groups of 10 people each and am choosing 10 people at random. What is the probability that all 10 people I have chosen are ...
86 views

### Quiz with questions sampled from a pool. How many new questions at each iteration? [duplicate]

I am taking a quiz which is a sample of $g$ questions from a pool of $n$ total questions. At every iteration $i$ I get a new sample of $g$ questions. I want to know the expected number of new ...
107 views

### Calculate probability that I have fully sampled a set [duplicate]

Let's say I have a set of items out of which I randomly take 5% . Then perform some action on these items and put them back in the set. After how many repetitions of this process can I be 95% sure ...
2k views

### Number of expected turns to get $k$ distinct numbers

We have a random number generator, which generates random numbers from $1$ to $N$. Each number has an equal probability of occurring (equiprobable). Find the expected number of turns to get $k$ ...
146 views

### Inverse coupon collector problem (estimating n), unequal case

I collect coupons of theoretically $n$ different colours, which come up randomly, one at a time. Up to now, I have collected $c$ coupons in total, falling into $j$ different colour classes. From this ...
5k views