Basic Definitions:
Random Variable: a function of samples in sample space, e.g. sum or product of dice value in a few consecutive die.
Probability Mass/Density Function: Probability of certain random variable's occurrence.
Cumulative Density Function: Accumulative probability of certain bounds of random variables' occurrence.
Expectation/Expected Value: Probability Weighted (e.g. average) value.
Variance: Probability Weighted (e.g. average) SQUARED distance (e.g. arithmetic distance) between random variable and Expected Value;
Standard Deviation: Squared Root of Variance