Essentials of Probability Theory for Statisticians provides
graduate students with a rigorous treatment of probability theory,
with an emphasis on results central to theoretical statistics. It
presents classical probability theory motivated with illustrative
examples in biostatistics, such as outlier tests, monitoring
clinical trials, and using adaptive methods to make design changes
based on accumulating data. The authors explain different methods
of proofs and show how they are useful for establishing classic
probability results. After building a foundation in probability,
the text intersperses examples that make seemingly esoteric
mathematical constructs more intuitive. These examples elucidate
essential elements in definitions and conditions in theorems. In
addition, counterexamples further clarify nuances in meaning and
expose common fallacies in logic. This text encourages students in
statistics and biostatistics to think carefully about probability.
It gives them the rigorous foundation necessary to provide valid
proofs and avoid paradoxes and nonsensical conclusions.
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