represents a binomial process with event probability p.
- BinomialProcess is a discrete-time and discrete-state process.
- BinomialProcess at time n is the number of events in the interval 0 to n.
- The number of events in the interval 0 to n follows BinomialDistribution[n,p].
- The times between events are independent and follow GeometricDistribution[p].
- BinomialProcess can be used with such functions as Mean, PDF, Probability, and RandomFunction.
Examplesopen allclose all
Basic Uses (5)
Process Slice Properties (6)
Univariate probability density:
Compare to the probability density of BinomialDistribution:
Multi-time slice distribution:
High-order probability density function:
Compute the expectation of an expression:
Calculate the probability of an event:
Find for what values of the parameter BinomialProcess is symmetric:
Find for what values of the parameter BinomialProcess is mesokurtic:
Moment has no closed form for symbolic order:
CentralMoment has no closed form for symbolic order:
FactorialMoment and its generating function:
Cumulant has no closed form for symbolic order:
A quality assurance inspector randomly selects a series of 10 parts from a manufacturing process that is known to produce 20% bad parts. Find the probability that the inspector gets at most one bad part:
The probability of selecting at most one bad part:
It is known that, on average, 50% of the residents in a city like a certain TV program. Find the probability that at least 55% of residents will report that they like a program, in a survey of 804 people from the city:
The probability that at least 55% of the residents in the sample will like the program:
A packet consisting of a string of symbols is transmitted over a noisy channel. Each symbol has a probability 0.0001 of being transmitted in error. Find the largest for which the probability of incorrect transmission (at least one symbol in error) is less than 0.001:
The probability of an error in the transmission:
Plot probability of a transmission error together with error limit:
Find the largest for which the probability of incorrect transmission is less than :
Find the price of a European call option after the third period in a multi-period binomial model, given that the initial price of the underlying is $100, strike price is $102, interest rate is 1% per period, and the stock moves up by 7% or down by a factor of 1/1.07:
Properties & Relations (5)
Binomial process is weakly stationary only for p equal to 0:
A BinomialProcess is the sum of a BernoulliProcess with :
Compare to the binomial process:
The time between events in a binomial process follows a PascalDistribution:
Calculate times between changes:
Compare the data histogram to the estimated probability density function:
Transition probability between two states:
BinomialProcess is a special case of CompoundRenewalProcess:
Create empirical covariance functions:
Wolfram Research (2012), BinomialProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/BinomialProcess.html.
Wolfram Language. 2012. "BinomialProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BinomialProcess.html.
Wolfram Language. (2012). BinomialProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BinomialProcess.html