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I'd be curious to know if there is a default random boolean generator in the random C++11 library. I've been using a int generator returning 0 or 1 and then converting to bool but I'm trying to optimize my code and thinking that I could save by using from the beginning a bool generator, if it exists.
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Theorem. Let X be a discrete random variable with a Bernoulli distribution with parameter p for some 0≤p≤1. Then the moment generating function MX of X is given by: MX(t)=q+pet.
Bernoulli Distribution Formula X can be written as X ∼ ∼ Bernoulli (p), where p is the parameter. The formulas for Bernoulli distribution are given by the probability mass function (pmf) and the cumulative distribution function (CDF).
The binomial distribution assumes that Y is the sum of independent random Bernoulli variables.
The expected value for a random variable, X, for a Bernoulli distribution is: E[X] = p. For example, if p = . 04, then E[X] = 0.04.
See std::bernoulli_distribution in the <random> header, aptly named after the Bernoulli distribution.
std::random_device device;
std::mt19937 gen(device());
std::bernoulli_distribution coin_flip(0.5);
bool outcome = coin_flip(gen);
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