2898411
| Frage | Antworten |
| \sigma-algebra | |
| probability measure | |
| measurable function | |
| random variable/random vector | |
| probability law/probability distribution | |
| cumulative distribution function | |
| probability density function | |
| random variables X and Y are identically distributed if... | |
| sub-\sigma-algebra | |
| independent (\sigma-algebra) | |
| independence (random variables) | |
| Lebesgue integration Step 1: Indicator functions | |
| Lebesgue Integration Step 2: simple functions | |
| Lebesgue Integration Step 3: non-negative random variables | |
| Lebesgue Integration Step 4: arbitrary random variables | |
| integrable | |
| null set | |
| Proof - see lecture notes | |
| Properties of the integral (five) | linearity domination triangle inequality set bounded integrability change of variable |
| Properties of the Integral/Expectation 1. Linearity | |
| Properties of the Integral/Expectation 2. Domination | |
| Properties of the Integral/Expectation 3. the triangle inequality | |
| Properties of the Integral/Expectation 4. Set bounded integrability | |
| Properties of the Integral/Expectation 5. Change of variable | |
| Dominated Convergence Theorem | |
| Monotone Convergence Theorem | |
| nth moment mean variance | |
| moment generating function | |
| Almost sure convergence | |
| mean square convergence | |
| Chebychev's Inequality | |
| Cauchy-Schwarz inequality | |
| convex function | |
| Jensen's inequality | |
| Proof - see notes | |
| Absolutely Continuous measure Equivalent measures | |
| Radon-Nikodym | |
| Radon-Nikodym derivative | |
| stochastic process | |
| integrable stochastic process |
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