## Basics of Bioinformatics: Lecture Notes of the Graduate by Rui Jiang, Xuegong Zhang, Michael Q. Zhang

By Rui Jiang, Xuegong Zhang, Michael Q. Zhang

This publication outlines eleven classes and 15 study themes in bioinformatics, in response to curriculums and talks in a graduate summer season institution on bioinformatics that used to be held in Tsinghua college. The classes comprise: fundamentals for Bioinformatics, simple records for Bioinformatics, themes in Computational Genomics, Statistical tools in Bioinformatics, Algorithms in Computational Biology, Multivariate Statistical equipment in Bioinformatics study, organization research for Human illnesses: tools and Examples, info Mining and information Discovery tools with Case Examples, utilized Bioinformatics instruments, Foundations for the examine of constitution and serve as of Proteins, Computational platforms Biology techniques for decoding conventional chinese language drugs, and complicated subject matters in Bioinformatics and Computational Biology. This e-book can function not just a primer for newcomers in bioinformatics, but in addition a hugely summarized but systematic reference ebook for researchers during this field.

Rui Jiang and Xuegong Zhang are either professors on the division of Automation, Tsinghua collage, China. Professor Michael Q. Zhang works on the chilly Spring Harbor Laboratory, chilly Spring Harbor, long island, USA.

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**Extra resources for Basics of Bioinformatics: Lecture Notes of the Graduate Summer School on Bioinformatics of China**

**Example text**

A random variable is a function from a sample space S into the real number space <. In defining a random variable, a new sample space (the range of the random variable) and a new probability function on this sample space are defined. We are interested in all possible values of a random variable, but we are more interested in the probabilities that the random variable takes these values. X Ä x/; for all x: This function is referred to the cumulative distribution function or cdf of X . x/: 1. limx!

X/ is a nondecreasing function of x: 3. x0 /: 0 These are sufficient and necessary conditions for a cdf. x/ is a step function. If two cdfs take equal values for all possible points in their common domains, we say that the corresponding random variables are identically distributed. X D a/ D 0 for any a 2 <. x/dx: a Of course, both pmf and pdf should be nonnegative and sum (integrate) to 1 for all possible values in their domains. In some cases we know the distribution of a random variable but are interested in some other quantities that can be mapped from this random variable.

Any function that satisfies the Axioms of Probability is a probability function. Let S D fs1 ; : : : ; sn g be a finite set and B be any sigma algebra of subset S. Let p1 ; : : : ; pn be nonnegative numbers that sum to 1. A/ D pi : fiWsi 2Ag Then P is a probability function on B. If p1 D p2 D D pn D 1=n, we have an equivalent form as the classical definition of probabilities. Many properties of the probability function can be derived from the Axioms of Probability. For example, for a single event A, we have: 1.