Math/Probability
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Probability space, Sample space, Event, and Elementary eventMath/Probability 2020. 2. 5. 12:33
1. Overview Probability space or a probability triple $(\Omega ,F,P)$ is a mathematical construct that models a real-world process (or “experiment”) consisting of states that occur randomly. Sample space (also called sample description space or possibility space) of an experiment or random trial is the set of all possible outcomes or results of that experiment. Event is a set of outcomes of an e..
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Conditional expectationMath/Probability 2020. 2. 5. 11:18
1. Overview In probability theory, the conditional expectation of a random variable is its expected value – the value it would take “on average” over an arbitrarily large number of occurrences – given that a certain set of "conditions" is known to occur 2. Description 2.1 Formula ith two random variables, if the expectation of a random variable X is expressed conditional on another random variab..
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Statistics and ProbabilityMath/Probability 2020. 1. 15. 22:12
1. Overview Statistics focuses predominantly on samples and incomplete data. Doing so brings some uncertainty to any of the results we reach. This uncertainty is what leads us to rely on some of the most important concepts of probability like expected values or prediction intervals. 2. Description 2.1 Relation Between Statistics and Probability In a way, probability lays the groundwork for stati..
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Bayes' Rule(Bayes' Theorem, Bayes' Law)Math/Probability 2019. 10. 14. 18:55
1. Overview In probability theory and statistics, Bayes’ theorem (alternatively Bayes’ law or Bayes’ rule) describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if cancer is related to age, then, using Bayes’ theorem, a person's age can be used to more accurately assess the probability that they have cancer than can be done..
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Dependent, independent event, and conditional probabilityMath/Probability 2019. 10. 14. 15:14
1. Overview 2. Description 2.1 Independent event The theoretical probability remains unaffected by other events 2.2 dependent event(=Conditional probability) $$P(A\: |\: B)$$ The probability of getting A, if we are given that B has occurred A given B 3. Example 4. References https://365datascience.co
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SetMath/Probability 2019. 10. 14. 13:09
1. Overview Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequnce of data. Bayesian in..
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CombinatoricsMath/Probability 2019. 10. 14. 11:03
1. Overview 2. Description 2.1 Permutation The number of different possible ways we can arrange a set of elements The order is crucial You always arrange the entire set of elements in the sample space $$P_{n}=n\times (n-1)\times (n-2)\times \cdots \times 1=n!$$ 2.2 Factorial $$n!=1\times 2\times 3\times \cdots \times n$$ The product of the natural numbers from 1 to n 2.2.1 Properties Negative nu..