BUILT-IN MATHEMATICA SYMBOL
Probability
Probability[pred, x
dist]
gives the probability for an event that satisfies the predicate pred under the assumption that x follows the probability distribution dist.
Probability[pred, xdata]
gives the probability for an event that satisfies the predicate pred under the assumption that x follows the probability distribution given by data.
Probability[pred, {x1, x2, ...}dist]
gives the probability that an event satisfies pred under the assumption that 
follows the multivariate distribution dist.
can be entered as x EscdistEsc dist or 
. 
can be entered as 
EsccondEsc 
or 
. - For a continuous distribution dist, the probability of pred is given by
where 
is the probability density function of dist and the integral is taken over the domain of dist.
- For a discrete distribution dist, the probability of pred is given by
where 
is the probability density function of dist and the summation is taken over the domain of dist.
- For a dataset data, the probability of pred is given by Sum[Boole[pred], {x, data}]/Length[data].
- Univariate data is given as a list of values
and multivariate data is given as a list of vectors 
.
- Probability[pred, {x1dist1, x2dist2}] corresponds to Probability[Probability[pred, x2dist2], x1dist1] so that the last variable is summed or integrated first.
- N[Probability[...]] calls NProbability for probabilities that cannot be evaluated symbolically.
- The following options can be given:
-
New in 8
, 
, ... are independent and follow the distributions 
, 
, ....
pred2, ...]
given 
.
