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  2. Balls into bins problem - Wikipedia

    en.wikipedia.org/wiki/Balls_into_bins_problem

    The efficiency of accessing a key depends on the length of its list. If we use a single hash function which selects locations with uniform probability, with high probability the longest chain has (⁡ ⁡ ⁡) keys. A possible improvement is to use two hash functions, and put each new key in the shorter of the two lists.

  3. Stars and bars (combinatorics) - Wikipedia

    en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)

    The solution to this particular problem is given by the binomial coefficient (+), which is the number of subsets of size k − 1 that can be formed from a set of size n + k − 1. If, for example, there are two balls and three bins, then the number of ways of placing the balls is ( 2 + 3 − 1 3 − 1 ) = ( 4 2 ) = 6 {\displaystyle {\tbinom {2 ...

  4. Problem of points - Wikipedia

    en.wikipedia.org/wiki/Problem_of_points

    The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory.One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value.

  5. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_distribution

    In probability theory, the Fourier transform of the probability distribution of a real-valued random variable is closely connected to the characteristic function of that variable, which is defined as the expected value of , as a function of the real variable (the frequency parameter of the Fourier transform).

  6. Campbell's theorem (probability) - Wikipedia

    en.wikipedia.org/wiki/Campbell's_theorem...

    In probability theory and statistics, Campbell's theorem or the Campbell–Hardy theorem is either a particular equation or set of results relating to the expectation of a function summed over a point process to an integral involving the mean measure of the point process, which allows for the calculation of expected value and variance of the random sum.

  7. List of probability distributions - Wikipedia

    en.wikipedia.org/wiki/List_of_probability...

    The Dirac delta function, although not strictly a probability distribution, is a limiting form of many continuous probability functions. It represents a discrete probability distribution concentrated at 0 — a degenerate distribution — it is a Distribution (mathematics) in the generalized function sense; but the notation treats it as if it ...

  8. Today's Wordle Hint, Answer for #1248 on Monday, November 18 ...

    www.aol.com/todays-wordle-hint-answer-1248...

    November 18, 2024 at 12:04 AM If you’re stuck on today’s Wordle answer, we’re here to help—but beware of spoilers for Wordle 1248 ahead. Let's start with a few hints.

  9. Mixture distribution - Wikipedia

    en.wikipedia.org/wiki/Mixture_distribution

    In probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized.