General

Symmetric

If there is a point that,

Then,

Is the expectation of this random variable, equal to the point of symmetry.

Median and Quantiles

The middle value of the random variable.
For median, set p to 0.5.

Variance

A positive quantity that measures the spread of the distribution of the random variable about its mean value.
Larger values of the variance indicate that the distribution is more spread out.

	Discrete	Continuous
Jointly Distributed	satisfying	satisfying
Joint Cumulative
Marginal Probability Distributions

Discrete

Probability Mass Function (PMF)

A set of probability value p_i assigned to each of the values taken by the discrete random variables x_i.

Probability

Expectation

Cumulative Distribution Function (CDF)

A set of probability value p_i assigned to each of the values taken by the discrete random variables x_i.

Continuous

Probability Density Function (PDF)

Probabilistic properties of a continuous random variable.

Expectation

Cumulative Distribution Function (CDF)

Probabilistic properties of a continuous random variable.