# Download A modern introduction to probability and statistics : by F M Dekking; et al PDF

By F M Dekking; et al

ISBN-10: 1852338962

ISBN-13: 9781852338961

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Extra info for A modern introduction to probability and statistics : understanding why and how

Example text

4............................ .. .. ... .... . .................. . ... ... 3..... ... ...... 1 ....... .. . . ... .... ... ... ... ..... ..... .. 2 ......... . . . ....... ... .......... ......... ... ... 3 ... .... . ... . 1 ... ... ... 2 ... ... . ... A C A∩C C A∩C A∩C A∩C A∩C C C C Ω Fig. 2. The law of total probability (illustration for m = 5). 2). Another, perhaps more pertinent, question about the BSE test is the following: suppose my cow tests positive; what is the probability it really has BSE?

The sum 1 + (1 − p) + · · · + (1 − p)n−1 + · · · is an example of a geometric series. It is well known that when |1 − p| < 1, 1 + (1 − p) + · · · + (1 − p)n−1 + · · · = Therefore we do indeed have P(Ω) = p · 1 = 1. p 1 1 = . 7 Suppose an experiment in a laboratory is repeated every day of the week until it is successful, the probability of success being p. The ﬁrst experiment is started on a Monday. What is the probability that the series ends on the next Sunday? 1 The sample space is Ω = {1234, 1243, 1324, 1342, .

2 ......... . . . ....... ... .......... ......... ... ... 3 ... .... . ... . 1 ... ... ... 2 ... ... . ... A C A∩C C A∩C A∩C A∩C A∩C C C C Ω Fig. 2. The law of total probability (illustration for m = 5). 2). Another, perhaps more pertinent, question about the BSE test is the following: suppose my cow tests positive; what is the probability it really has BSE? Translated, this asks for the value of P(B | T ). The information we were given is P(T | B), a conditional probability, but the wrong one.