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.

0 ≤ p_i ≤ 1 and ∑ p_i = 1

Probability
$p_i$

Expectation
 

Cumulative Distribution Function (CDF)

Continuous

Probability Density Function (PDF)

Probabilistic properties of a continuous random variable.

Expectation
 

Cumulative Distribution Function (CDF)

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.