Bernoulli distribution

The first part concludes with what is now known as the Bernoulli distribution.

In this case it degenerates into a Bernoulli distribution with .

Thus the measure is used to evaluate how data compares to a fixed-probability-of-success Bernoulli distribution.

They all have the same Bernoulli distribution.

If then has a Bernoulli distribution with parameter .

It is the generalization of the Bernoulli distribution for a categorical random variable.

The Bernoulli distributions, (number of successes in one trial with probability p of success).

The Bernoulli distributions for form an exponential family.

Bernoulli distribution is a special case of the Binomial distribution with .

The Bernoulli distribution is simply .

The Beta distribution is the conjugate prior of the Bernoulli distribution.

Binary variables that are random variables are distributed according to a Bernoulli distribution.

Bernoulli distribution, a discrete probability distribution which compels the random variable to take one of two values.

We can create a mixture model with different components, where each component is a vector of size of Bernoulli distributions (one per pixel).

In some contexts, uncorrelatedness implies at least pairwise independence (as when the random variables involved have Bernoulli distributions).

For discrete features like the ones encountered in document classification (include spam filtering), multinomial and Bernoulli distributions are popular.

Bernoulli distribution and Log-normal distribution.

Bernoulli distribution, Power distribution.

Every cumulant is just n times the corresponding cumulant of the corresponding Bernoulli distribution.

Bernoulli distribution, for the outcome of a single Bernoulli trial (e.g. success/failure, yes/no)

Equality holds only for the two point Bernoulli distribution or the sum of two different Dirac delta functions.

The distribution is a special case of a "multivariate Bernoulli distribution" in which exactly one of the k 0-1 variables takes the value one.

The categorical distribution is the generalization of the Bernoulli distribution for variables with any constant number of discrete values.

When the observations are independent, this estimator has a (scaled) binomial distribution (and is also the sample mean of data from a Bernoulli distribution).

For instance, if one is using a beta distribution to model the distribution of the parameter p of a Bernoulli distribution, then: