Examples for

Probability Distributions

Probability distributions are functions that describe the likelihood of different outcomes of random phenomena in terms of how probable they are to occur. Wolfram|Alpha's exhaustive computational knowledge of both discrete probability mass functions and continuous probability distribution functions allows you to visualize relative probabilities and compute moments, expected values, standard deviations and all manner of observable properties of a wide range of distributions.
Continuous Distributions

Analyze properties, find moments and determine the likelihood of outcomes of continuous distributions.

Compute properties of a continuous distribution:

beta distribution

Specify parameters for a distribution:

normal distribution, mean=0, sd=2
hyperbolic distribution shape=1 skewness=0 scale=1 location=0

Compute a particular property:

characteristic function of an exponential distribution
standard deviation of Student t, 17 degrees of freedom
moyal distribution mu=2.3 sigma=12 skewness

Compute a moment of a distribution:

2nd moment F distribution n=12 m=8

Compute a central moment:

5th central moment of chi-square dist

Compute a cumulant:

4th cumulant, Rayleigh dist
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Discrete Distributions

Analyze properties, find moments and determine the likelihood of outcomes of discrete distributions.

Compute properties of a discrete distribution:

Poisson distribution

Specify parameters for a distribution:

binomial distribution n=40, p=0.32

Compute a particular property:

mean Zipf distribution, rho=2
survival function pascal distribution

Compute a moment of a distribution:

3rd moment Benford dist b=8
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