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Buffon's needle was the earliest problem in geometric probability to be solved; [2] it can be solved using integral geometry. The solution for the sought probability p, in the case where the needle length l is not greater than the width t of the strips, is. This can be used to design a Monte Carlo method for approximating the number π ...
An Essay Towards Solving a Problem in the Doctrine of Chances. An Essay Towards Solving a Problem in the Doctrine of Chances is a work on the mathematical theory of probability by Thomas Bayes, published in 1763, [1] two years after its author's death, and containing multiple amendments and additions due to his friend Richard Price. The title ...
Multiple comparisons problem. An example of coincidence produced by data dredging (uncorrected multiple comparisons) showing a correlation between the number of letters in a spelling bee's winning word and the number of people in the United States killed by venomous spiders. Given a large enough pool of variables for the same time period, it is ...
In probability theory and statistics, the conditional probability distribution is a probability distribution that describes the probability of an outcome given the occurrence of a particular event. Given two jointly distributed random variables and , the conditional probability distribution of given is the probability distribution of when is ...
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1-p).
The Poisson distribution is an appropriate model if the following assumptions are true: k is the number of times an event occurs in an interval and k can take values 0, 1, 2, ... . The occurrence of one event does not affect the probability that a second event will occur. That is, events occur independently.
Sensitivity (true positive rate) is the probability of a positive test result, conditioned on the individual truly being positive. Specificity (true negative rate) is the probability of a negative test result, conditioned on the individual truly being negative. If the true status of the condition cannot be known, sensitivity and specificity can ...
Secretary problem. Graphs of probabilities of getting the best candidate (red circles) from n applications, and k / n (blue crosses) where k is the sample size. The secretary problem demonstrates a scenario involving optimal stopping theory [1][2] that is studied extensively in the fields of applied probability, statistics, and decision theory.