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The Bernoulli Distribution
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The Bernoulli Distribution
The Bernoulli distribution is the simplest of the discrete
probability distributions. It has two possible outcomes: 0
('failure') and 1 ('success'). It has a single parameter,
p, that specifies the probability of success.
Bernoullior example, the distribution of heads and tails in
coin tossing has a Bernoulli distribution with p = 0.5.
The probability of a newborn to be a girl has a probability
distribution with p = 0.48 (approximately).
Being the simplest discrete distribution, the Bernoulli
distribution is the basic building block for several other discrete
probability distributions:
The Bernoulli distribution is implemented by the
BernoulliDistribution class. It has one constructor
which has one parameter: the probability of success of a trial. The
probability must be between 0 and 1. The following constructs a
Bernoulli distribution with probability of success 0.4:
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BernoulliDistribution bernoulli = new BernoulliDistribution(0.4); |
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Dim bernoulli As BernoulliDistribution = New BernoulliDistribution(0.4)
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The BernoulliDistribution class has one specific
property,
ProbabilityOfSuccess, which returns the probabiltiy of
success of a trial.
BernoulliDistribution has one static
(Shared in Visual Basic) method,
GetRandomVariate, which generates a random variate using
a user-supplied uniform random number generator.
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MersenneTwister random = new MersenneTwister();
double variate = BernoulliDistribution.GetRandomVariate(random, 0.4); |
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Dim random As MersenneTwister = New MersenneTwister()
Dim variate As Double = BernoulliDistribution.GetRandomVariate(random, 0.4) |
The above example uses the Mersenne
Twister to generate uniform random numbers.
For details of the properties and methods common to all discrete
probability distribution classes, see the topic on DiscreteDistribution
class.