Notation:

Set intersection of two sets A and B denoted by A ∩ B is the subset of A or B that contains all elements that are in both A and B, i.e. A ∩ B := { x : x in A and x in B}.

Set union of two sets A and B denoted by A ∪ B is the set that contains precisely the elements that are in A or in B, i.e A ∪ B := { x : x in A or x in B}.

Set difference of the two sets A and B denoted by A – B or AB is the subset of A that contains all elements in A that are not in B, i.e. A – B := { x : x in A and x not in B}.

Summation symbol ∑ represents the sum of all members over the set, e.g.:

Definitions and terms:

• Population: A set of the similar data or items subject to the analysis.
• Sample: A subset of the population.
• Arithmetic mean (average) of a set: The sum of all the values in the set divided by the size of the set
• Median: The middle value in an ordered set, for example, the median of the set {x₁, …, x_2k+1} where x₁ <…< x_2k+1 is the value x_k+1.
• Random variable: A function from the set of possible outcomes to the set of the values (for example, real numbers).
• Expectation: An expectation of a random variable is the limit of the average values of the increasing sets of the values given by the random variable.
• Variance: Measures the dispersion of the population from its mean. Mathematically, the variance of a random variable X is the expected value of the square of the difference between the random variable and the mean μ of X, i.e. Var(X) = E[(X - μ)²].
• Standard deviation: The deviation of the random variable X is the square root of the variation of the variable X, i.e. SD(X)=sqrt(Var(X)).
• Correlation: The measure of the dependency between the random variables. Mathematically, for the random variables X and Y, the correlation is defined as corr(X,Y) = E[(X - μ_X) * (Y-μ_Y)]/(SD(X) * SD(Y)).
• Causation: A dependence relation explaining the occurrence of one phenomena through the occurrence of another phenomena. Causation implies correlation, but not vice versa!
• Slope: The variable a in the linear equation y=a*x+b.
• Intercept: The variable b in the linear equation y=a*x+b.