Linked Questions

2
votes
1answer
3k views

Expected coverage after sampling with replacement 'k' times [duplicate]

Possible Duplicate: probability distribution of coverage of a set after X independently, randomly selected members of the set If I sample with replacement $k$ ...
7
votes
1answer
2k views

The exact probability of observing $x$ unique elements after sampling with replacement from a set with $N$ elements

Say I sample with replacement from a set of $N$ unique elements s.t. elements are selected with uniform probability. If I sample with replacement $M$ times from this set, what is the exact ...
4
votes
1answer
3k views

Statistical Inference Question

From Statistical Inference Second Edition (George Casella, Roger L. Berger) "My telephone rings 12 times each week, the calls being randomly distributed among the 7 days. What is the probability that ...
3
votes
1answer
974 views

Estimate the number of elements by random sampling with replacement

Setup: $N$ numbered balls are in a bag. $N$ is unknown. Pick a ball uniformly at random, record its number, replace it, shuffle. After $M$ samples, of which we noticed $R$ repeated numbers, how can ...
3
votes
2answers
385 views

Probability of having 'k' elements that occur only once in a multiset filled by sampling with replacement

Let's say that I have a set of unique elements, $P$, and a multiset $M$ that I fill with $N \leq ||P||$ elements by sampling with replacement from $P$. What is the probability that the multiset $M$ ...
1
vote
1answer
230 views

Probability distribution for sampling an element $k$ times after $x$ independent random samplings with replacement

In an earlier question ( probability distribution of coverage of a set after `X` independently, randomly selected members of the set ), Ross Rogers asked for the probability distribution for the ...
1
vote
1answer
131 views

Basic probability question on repetition of an experiment

Suppose an experiment has $N$ possible outcomes, each with probability $1/N$. If I repeat the experiment $a N$ times where $a$ is a whole number, what is the probability that every single one of the $...
0
votes
1answer
106 views

Number of Unique Elements After Sampling w. Replacement

Consider the set $N=\{1,\ldots, n\}$. Let $p_n(m,k)$ denote the probability that we have $m$ unique elements from $N$ after $x$ draws (with replacement). As per this post, we explicitly have $$p_n(m,x)...
1
vote
1answer
71 views

What is probability that a sample covers all classes?

Suppose: there are $n$ distinct classes in a population (i.e. each member of the population is a member of exactly one class), (For simplicity) the classes are all equally sized and the probability ...
0
votes
0answers
36 views

What is the probability of rolling at least 4 of each number on a dice after x rolls

I've been using Stirling numbers of the second kind in an approach to find the probability of rolling at least one of each number after x rolls as suggested by Henry probability distribution of ...
0
votes
1answer
32 views

The probability that the size of a set is N after observing M unique elements from a sample of X (with replacement)

Problem Given a set of unknown size, X elements are sampled with replacement. Of these sampled elements, M elements are unique, meaning (X - M) elements were chosen more than once. Knowing this, what ...