Editing Operators (section)

== Probability and Statistics Operators ==
* Expected Value (E)
** Mean value of a random variable.
*** Estimating outcomes, decision-making.

* Variance (Var)
** Measure of how spread out the values in a data set are around the mean.
*** Assessing risk, quantifying variability.

* Standard Deviation (σ or SD)
** Square root of the variance.
*** Measuring dispersion, error bars in plots.

* Probability (P)
** Measure of the likelihood of an event occurring.
*** Assessing uncertainty, predicting outcomes.

* Conditional Probability (P(A|B))
** Probability of event A occurring given that event B has already occurred.
*** Bayesian inference, probability trees.

* Joint Probability (P(A ∩ B))
** Probability of both events A and B occurring simultaneously.
*** Probability distribution functions, contingency tables.

* Marginal Probability (P(A))
** Probability of a single event occurring regardless of other events.
*** Summing joint probabilities, independence testing.

* Cumulative Distribution Function (CDF)
** Function that maps the probability of a random variable being less than or equal to a certain value.
*** Probability distribution functions, hypothesis testing.

* Probability Density Function (PDF)
** Function that describes the likelihood of a random variable taking on a particular value.
*** Modeling continuous random variables, integration.

* Covariance
** Measure of the joint variability of two random variables.
*** Assessing correlation, portfolio management.

* Correlation
** Measure of the strength and direction of the relationship between two random variables.
*** Analyzing relationships, predictive modeling.