- Story. A Bernoulli trial is an experiment that has two outcomes that can be encoded as success (\(y=1\)) or failure (\(y=0\)). The result \(y\) of a Bernoulli trial is Bernoulli distributed.
- Example. Check to see if a given bacterium is competent, given that it has probability \(θ\) of being competent.
- Parameter. The Bernoulli distribution is parametrized by a single value, \(θ\), the probability that the trial is successful.
- Support. The Bernoulli distribution may be nonzero only for zero and one.
- Probability mass function.
\(\begin{align}
f(y;\theta) = \left\{ \begin{array}{ccc}
1-\theta & & y = 0 \\(0.5em]
\theta & & y = 1.
\end{array}
\right.
\end{align}\)
- Usage
| Package |
Syntax |
| NumPy |
np.random.choice([0, 1], p=[1-theta, theta]) |
| SciPy |
scipy.stats.bernoulli(theta) |
| Stan |
bernoulli(theta) |
- Related distributions.
- The Bernoulli distribution is a special case of the Binomial distribution with \(N=1\).
params = [dict(name='θ', start=0, end=1, value=0.5, step=0.01)]
app = distribution_plot_app(x_min=0,
x_max=1,
scipy_dist=st.bernoulli,
params=params,
x_axis_label='y',
title='Bernoulli')
bokeh.io.show(app, notebook_url=notebook_url)