Probability Theory and Statistics

Probability Theory andStatisticsWith a view towards the natural sciencesLecture notesNiels Richard HansenDepartment of Mathematical SciencesUniversity of CopenhagenNovember 20102 PrefaceThe present lecture notes have been developed over the last couple of years for acourse aimed primarily at the students taking a Master s in bioinformatics at theUniversity of Copenhagen. There is an increasing demand fora general introductorystatistics course at the Master s level at the university, and the course has alsobecome a compulsory course for the Master s in eScience. Both educations emphasizea computational and data oriented approach to science in particular the aim of the notes is to combine the mathematical and theoretical underpinningof Statistics and statistical data analysis with computational methodology and prac-tical applications. Hopefully the notes pave the way for an understanding of thefoundation of data analysis with a focus on the probabilistic model and the method-ology that we can develop from this point of view.

The Yahtzee problem can in principle be solved by counting – simply write down all combinations and count the number of favorable and possible combinations. Then the pseudo theorem applies. It is a futile task but in principle a possibility. In many cases it is, however, impossible to rely on counting – even in principle. As

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