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 |