Search results
Results From The WOW.Com Content Network
In probability theory, the expected value ... rules for how to calculate expectations in more ... of rolls of a dice to the expected value of 3.5 as the number of ...
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.
These equations can be used to calculate and chart the probability of exactly q and at least q for any or multiple n. For most purposes, it is sufficient to know the following facts of dice probability: The expected quantity of any face value among a number of unknown dice is one-sixth the total unknown dice.
In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein each of some finite whole number n of outcome values are equally likely to be observed. Thus every one of the n outcome values has equal probability 1/n. Intuitively, a discrete uniform distribution is "a known, finite number ...
This theorem makes rigorous the intuitive notion of probability as the expected long-run relative frequency of an event's occurrence. It is a special case of any of several more general laws of large numbers in probability theory. Chebyshev's inequality. Let X be a random variable with finite expected value μ and finite non-zero variance σ 2.
We know the expected value exists. The dice throws are randomly distributed and independent of each other. So simple Monte Carlo is applicable: s = 0; for i = 1 to n do throw the three dice until T is met or first exceeded; r i = the number of throws; s = s + r i; repeat m = s / n; If n is large enough, m will be within ε of μ for any ε > 0.
A probability is a way of assigning every event a value between zero and one, with the requirement that the event made up of all possible results (in our example, the event {1,2,3,4,5,6}) is assigned a value of one. To qualify as a probability, the assignment of values must satisfy the requirement that for any collection of mutually exclusive ...
As the factory is improved, the dice become less and less loaded, and the outcomes from tossing a newly produced die will follow the uniform distribution more and more closely. Tossing coins; Let X n be the fraction of heads after tossing up an unbiased coin n times. Then X 1 has the Bernoulli distribution with expected value μ = 0.5 and ...