## 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.

### Covariance

Independent random variables have a covariance of zero.

### Correlation

Values between -1 and 1, and independent random variables have a correlation of zero.

What if random variable X and Y have linear relationship, that is

That is,

## Distribution Function

| Discrete | Continuous
Probability A set of probability value pi assigned to each of the values taken by the discrete random variables xi. | Probability Mass Function (PMF) Probability Expectation | Probability Density Function (PDF) Probabilistic properties of a continuous random variable. Expectation
Cumulative A set of probability value pi assigned to each of the values taken by the discrete random variables xi. |  |
Jointly Distributed | satisfying | satisfying
Joint Cumulative |  |
Marginal Probability Obtained by summing or integrating the joint probability distribution over the values of the other random variable. |  |
Conditional Probability The probabilistic properties of the random variable X under the knowledge provided by the value of Y. |  |
Independence Two random variables X and Y are said to be independent if: | for all values i of X and j of Y. | for all X and Y.