Category Archives: Probability

Karl Popper: Conjectures and Refutations

(1) It is easy to obtain confirmations, or verifications, for nearly every theory-if we look for confirmations. (2) Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in … Continue reading

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Expectation: Useful properties and inequalities

If is a random variable on . The expected value of is defined as Inequalities Jensen’s inequality. If is convex and Holder’s inequality. If with then Cauchy-Schwarz Inequality: For

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A nice chart of univariate distribution relationships

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Very brief notes on measures: From σ-fields to Carathéodory’s Theorem

Definition 1. A -field is a non-empty collection of subsets of the sample space closed under the formation of complements and countable unions (or equivalently of countable intesections – note ). Hence is a -field if whenever whenever Definition 2. … Continue reading

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