By Steve Dobbs
Written to compare the contents of the Cambridge syllabus. data 1 corresponds to unit S1. It covers illustration of knowledge, diversifications and mixtures, likelihood, discrete random variables and the traditional distribution.
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Additional resources for Advanced Level Mathematics: Statistics 1
The reports have no individual credibility if i ¼ P(H ) ¼ 1/n. Plugging this into the equation above yields P(H/E1,E2) ¼ 1/n ¼ P(H ). Hence, nothing is gained, as far as posterior probability is concerned, by combining independent reports that are individually useless: the result of such combination will be just as worthless as the original reports uncombined. coherence, truth, and testimony 31 It is worth noting that this negative result relies on the other assumptions that are part of Huemer’s model and that it does not just make use of the assumed individual uselessness of the reports.
The testimonies are independent, in the relevant sense, just in case there is no inﬂuence between them given that Forbes’s guilt has been decided. This amounts to saying that they are conditionally independent in our sense of P(E1/H ) ¼ P(E1/H,E2) and PðE1 =:HÞ ¼ PðE1 =:H, E2 Þ. 1). e. 1: Independent testimonies. Smith’s and Jones’s testimonies are directly inﬂuenced by the fact they are reporting on. There is no direct inﬂuence between the testimonies themselves. coherence, truth, and testimony 29 probability of what is being said?
Take a case of two witnesses, Smith and Jones, testifying individually to the effect that another man, Forbes, has committed a certain crime. Now if this is not a case of coherence, then, I must confess, I have no idea of what that notion could possibly involve. After all, the witnesses say exactly the same thing, and so what they say could hardly be in greater ‘harmony’, exhibit greater ‘mutual support’, or ‘hang better together’, to refer to some of the usual characterizations of coherent sets.
Advanced Level Mathematics: Statistics 1 by Steve Dobbs