Math
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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..
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ProbabilityMath/Probability 2019. 10. 14. 10:07
1. Overview Probability is a measure quantifying the likelihood that events will occur. See glossary of probability and statistics. Probability quantifies as a number between 0 and 1, where, roughly speaking, 0 indicates impossibility and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbi..
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Quadratic formMath/Linear algebra 2019. 10. 13. 21:21
1. Overview all matrix is square 2. Description 3. Example What do they mean and how do you interpret them? So this is related to the concept of the energy in matrix S that I referred to. If symmetric 3 by 3 matrix identity matrix 4. Quadratic form in geometry You should also note that all of these surfaces have a value of zero at the coordinate point W1 W2 both equals 0. And that's because when..
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Condition numberMath/Linear algebra 2019. 10. 13. 21:04
1. Overview 2. Description In fact, one way to interpret that condition number is as an indicator of the dominance of large scale structure in the matrix. now the condition number is really small is a well-conditioned matrix but this matrix doesn't really contain any useful information. It doesn't actually contain any meaningful patterns it's literally just noise. In this video, 3. Example 4. Re..
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Projections in RN spaceMath/Linear algebra 2019. 10. 12. 11:59
1. Overview A projection is a linear transformation P from a vector space to itself such that$P^{2}=P$. That is, whenever P is applied twice to any value, it gives the same result as if it were applied once (idempotent). It leaves its image unchanged. Though abstract, this definition of "projection" formalizes and generalizes the idea of graphical projection. One can also consider the effect of ..