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The Bernoulli distribution is a discrete probability distribution which takes on two values, 0 and 1. The value 1 occurs with probability \(p\), and 0 occurs with probabilty \(1-p\).
It is equivalent to the \({\it Binomial}(1,p)\) distribution (see Binomial Random Variable)
Returns the value at x of the probability function of a \({\it Bernoulli}(p)\) random variable, with \(0 \leq p \leq 1\).
The \({\it Bernoulli}(p)\) random variable is equivalent to the \({\it Binomial}(1,p)\) .
The mean is
(%i1) load ("distrib")$
(%i2) pdf_bernoulli(1,p); (%o2) p
Returns the value at x of the distribution function of a
\({\it Bernoulli}(p)\)
random variable, with \(0 \leq p \leq 1\). To make use of this function, write first load("distrib")
.
The cdf is
Returns the q-quantile of a
\({\it Bernoulli}(p)\)
random variable, with \(0 \leq p \leq 1\); in other words, this is the inverse of cdf_bernoulli
. Argument q must be an element of \([0,1]\). To make use of this function, write first load("distrib")
.
Returns the mean of a \({\it Bernoulli}(p)\) random variable, with \(0 \leq p \leq 1\).
The \({\it Bernoulli}(p)\) random variable is equivalent to the \({\it Binomial}(1,p)\) .
The mean is
(%i1) load ("distrib")$
(%i2) mean_bernoulli(p); (%o2) p
Returns the variance of a \({\it Bernoulli}(p)\) random variable, with \(0 \leq p \leq 1\).
The \({\it Bernoulli}(p)\) random variable is equivalent to the \({\it Binomial}(1,p)\) .
The variance is
(%i1) load ("distrib")$
(%i2) var_bernoulli(p); (%o2) (1 - p) p
Returns the standard deviation of a \({\it Bernoulli}(p)\) random variable, with \(0 \leq p \leq 1\).
The \({\it Bernoulli}(p)\) random variable is equivalent to the \({\it Binomial}(1,p)\) .
The standard deviation is
(%i1) load ("distrib")$
(%i2) std_bernoulli(p); (%o2) sqrt((1 - p) p)
Returns the skewness coefficient of a \({\it Bernoulli}(p)\) random variable, with \(0 \leq p \leq 1\).
The \({\it Bernoulli}(p)\) random variable is equivalent to the \({\it Binomial}(1,p)\) .
The skewness coefficient is
(%i1) load ("distrib")$
(%i2) skewness_bernoulli(p); 1 - 2 p (%o2) --------------- sqrt((1 - p) p)
Returns the kurtosis coefficient of a \({\it Bernoulli}(p)\) random variable, with \(0 \leq p \leq 1\).
The \({\it Bernoulli}(p)\) random variable is equivalent to the \({\it Binomial}(1,p)\) .
The kurtosis coefficient is
(%i1) load ("distrib")$
(%i2) kurtosis_bernoulli(p); 1 - 6 (1 - p) p (%o2) --------------- (1 - p) p
Returns a
\({\it Bernoulli}(p)\)
random variate, with \(0 \leq p \leq 1\). Calling random_bernoulli
with a second argument n, a random sample of size n will be simulated.
This is a direct application of the random
built-in Maxima function.
See also random
. To make use of this function, write first load("distrib")
.
Next: Geometric Random Variable, Previous: Poisson Random Variable, Up: Functions and Variables for discrete distributions [Contents][Index]