A probability distribution for a random variable describes how probabilities
are distributed over the possible values of the random variable.
Summary measures of a probability distribution are mean (central tendency),
Variance (dispersion or spread) and Skewness or Kurtosis (shape).
$$X: {x_1, x_2 … x_n}$$
$$P: {p_1, p_2 … p_n}$$
$$Mean=E(X)= µ_x=\sum_{i=1}^n p_i x_i $$
$$Variance= Var(X)= σ_x^2=\sum_{i=1}^n p_i (x_i-µ_x)^2= \sum_{i=1}^n p_ix_i^2-µ_x^2 $$
The relationship between mean and variance for linear functions is:
$$Y=α+βX$$
$$E(Y)= α+βE(X)$$
$$Var(Y)= β^2 Var(X)$$
