Convergence
From the introductory chapter we remember that the basis of probability theory, the empirical basis upon which the modeling of random phenomena rests, is the stabilization of the relative frequencies. In statistics a rule of thumb is to base one’s decisio
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Allan Gut
Probability: A Graduate Course Second Edition
123
Allan Gut Department of Mathematics Uppsala University Uppsala Sweden
ISSN 1431-875X ISBN 978-1-4614-4707-8 DOI 10.1007/978-1-4614-4708-5
ISBN 978-1-4614-4708-5
(eBook)
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Preface to the First Edition
Toss a symmetric coin twice. What is the probability that both tosses will yield a head? This is a well-known problem that anyone can solve. Namely, the probability of a head in each toss is 1=2, so the probability of two consecutive heads is 1=2 1=2 ¼ 1=4. BUT! What did we do? What is involved in the solution? What are the arguments behind our computations? Why did we multiply the two halves connected with each toss? This is reminiscent of the centipede1 who was asked by another animal how he walks; he who has so many legs, in which order does he move them as he is walking? The centipede contemplated the question for a while, but found no answer. However, from that moment on he could no longer walk. This book is written with the hope that we are not centipe
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