A Symbols used

A.1 Symbols and abbreviations used

Range space for rv \(X\): \(\mathcal{R}_X\)

Symbol Meaning Reference
\(\in\) Is an element of Chap. 1
\(\subset\) Proper subset Chap. 1
\(\subseteq\) Subset Chap. 1
\(\cup\) Set union; or Chap. 1
\(\cap\) Set intersection; and Chap. 1
\(A\setminus B\) Set difference Chap. 1
Superscript \(c\) Set complement Chap. 1
\(|A|\) Cardinality of set \(A\) Chap. 1
\(\aleph_0\) The smallest infinite cardinality Chap. 1
\(\mathfrak{c}\) Cardinality of the continuum Chap. 1
\(\mathbb{N}\) Set of natural (counting) numbers Chap. 1
\(\mathbb{Z}\) Set of integers Chap. 1
\(\mathbb{Q}\) Set rational numbers Chap. 1
\(\mathbb{R}\) Set of real numbers Chap. 1
\(\mathbb{R}^{+}_0\) Set of non-negative real numbers Chap. 1
\(\mathbb{R}_{+}\) Set of positive real numbers Chap. 1
\(\mathbb{R}_{-}\) Set of negative real numbers Chap. 1
\(\mathbb{C}\) Set of complex numbers Chap. 1
\(P^n_r\) Permutation of \(r\) elements from \(n\) Chap. 2
\(C^n_r\); \(\binom{n}{r}\) Combination of \(r\) elements from \(n\) Chap. 2
\(p_X(x)\) Probability mass function of \(X\) Chap. 2
\(f_X(x)\) Probability density function of \(X\) Chap. 2
\(F_X(x)\) Distribution function for \(X\) Chap. 2
\(\operatorname{E}[X]\); \(\mu\) Expected value, or mean, of \(X\) Chap. 3
\(\operatorname{var}[X]\); \(\sigma^2\) Variance of \(X\) Chap. 3
\(\gamma_1\) Skewness Chap. 3
\(\gamma_2\) Excess kurtosis Chap. 5
\(M_X(t)\) Moment-generating function Chap. 5
\(\mu'_r\) \(r\)th raw moment Chap. 5
\(\mu_r\) \(r\)th central moment Chap. 5
\(\phi(\cdot)\) Standard normal density function Chap. 8
\(\Phi(\cdot)\) Cumulative standard normal distribution function Chap. 8
\(\operatorname{erf}(x)\) Error function Chap. 8