Search results
Results from the WOW.Com Content Network
A gambler's fortune (capital) is a martingale if all the betting games which the gambler plays are fair. The gambler is playing a game of coin flipping. Suppose X n is the gambler's fortune after n tosses of a fair coin, such that the gambler wins $1 if the coin toss outcome is heads and loses $1 if the coin toss outcome is tails. The gambler's ...
Tossing a coin. Coin flipping, coin tossing, or heads or tails is the practice of throwing a coin in the air and checking which side is showing when it lands, in order to randomly choose between two alternatives. It is a form of sortition which inherently has two possible outcomes. The party who calls the side that is facing up when the coin ...
The parameter is the probability that a coin lands heads up ("H") when tossed. can take on any value within the range 0.0 to 1.0. For a perfectly fair coin, =. Imagine flipping a fair coin twice, and observing two heads in two tosses ("HH"). Assuming that each successive coin flip is i.i.d., then the probability of observing HH is (=) = =
In probability theory, stochastic drift is the change of the average value of a stochastic (random) process. A related concept is the drift rate, which is the rate at which the average changes. For example, a process that counts the number of heads in a series of fair coin tosses has a drift rate of 1/2 per toss. This is in contrast to the ...
It can be used to represent a (possibly biased) coin toss where 1 and 0 would represent "heads" and "tails", respectively, and p would be the probability of the coin landing on heads (or vice versa where 1 would represent tails and p would be the probability of tails). In particular, unfair coins would have /
The Bernoulli process, which can serve as a mathematical model for flipping a biased coin, is possibly the first stochastic process to have been studied. [81] The process is a sequence of independent Bernoulli trials, [ 82 ] which are named after Jacob Bernoulli who used them to study games of chance, including probability problems proposed and ...
The entropy of the unknown result of the next toss of the coin is maximized if the coin is fair (that is, if heads and tails both have equal probability 1/2). This is the situation of maximum uncertainty as it is most difficult to predict the outcome of the next toss; the result of each toss of the coin delivers one full bit of information.
In the theory of stochastic processes in discrete time, a part of the mathematical theory of probability, the Doob decomposition theorem gives a unique decomposition of every adapted and integrable stochastic process as the sum of a martingale and a predictable process (or "drift") starting at zero.