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   Discover the best free online games at AOL.com - Play board, card, casino, puzzle and many more online games while chatting with others in real-time.

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4. Lottery (decision theory) - Wikipedia

   en.wikipedia.org/wiki/Lottery_(decision_theory)

   In expected utility theory, a lottery is a discrete distribution of probability on a set of states of nature.The elements of a lottery correspond to the probabilities that each of the states of nature will occur, (e.g. Rain: 0.70, No Rain: 0.30). [1]

5. Conditional probability distribution - Wikipedia

   en.wikipedia.org/wiki/Conditional_probability...

   Seen as a function of for given , (= | =) is a probability mass function and so the sum over all (or integral if it is a conditional probability density) is 1. Seen as a function of x {\displaystyle x} for given y {\displaystyle y} , it is a likelihood function , so that the sum (or integral) over all x {\displaystyle x} need not be 1.

6. 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.

7. Martingale (probability theory) - Wikipedia

   en.wikipedia.org/wiki/Martingale_(probability...

   This can be used to show that the gambler's total gain or loss varies roughly between plus or minus the square root of the number of games of coin flipping played. de Moivre's martingale: Suppose the coin toss outcomes are unfair, i.e., biased, with probability p of coming up heads and probability q = 1 − p of tails. Let

8. Bernoulli distribution - Wikipedia

   en.wikipedia.org/wiki/Bernoulli_distribution

   In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, [1] is the discrete probability distribution of a random variable which takes the value 1 with probability and the value 0 with probability =.

9. Free probability - Wikipedia

   en.wikipedia.org/wiki/Free_probability

   Free probability is a mathematical theory that studies non-commutative random variables. The "freeness" or free independence property is the analogue of the classical notion of independence , and it is connected with free products .