The material in this book is mainly targeted towards the laymen, not really some startling enlightenment for some scientists. Nevertheless, the author has packaged some fundamental statistical and probabilistic knowledge as well as some insightful observations and opinions into a few interesting "laws": "The Law of Inevitability", "The Law of Truly Large Numbers", "The Law of Selection", "The Law of the Probability Lever" and the "Law of Near Enough".
The slight disappointment is that I somehow had expected the book might teach me something more profound about the probability, like what Brian Greene has done (about quantum mechanics and not to mention the superstring theory) in his book "The Fabric of the Cosmos". But in this book, the author primarily seems to be interested to dispense with superstition and misconception of the improbable from the public. Though what has been written is still intriguing and interesting in some sense, it doesn't really teach me (a physicist) something fundamentally new.
On p.180, lines 3-5, it says "the exact probability that the flagged transaction is actually a misclassified legitimate one is 91 percent". It's taken me some time (like a student learning probability) to obtain this number with Bayes' Theorem. Let "L", "F" and "D" denote "legitimate transactions", "fraudulent transactions' and "flagged as fraudulent" respectively. From the 3rd last line on p.179, P(F) = 0.001 and P(L) = 1 - 0.001 = 0.999. Bayes' Theorem tells us that P(L/D) = P(D/L) P(L) / P(D). From the 2nd last paragraph on p.179, P(D/L) = 1 - 0.99 = 0.01 and P(D/F) = 0.99. From the Total Probability Theorem and with the aforementioned probabilities, P(D) = P(D/L) P(L) + P(D/F) P(F) ) = 0.01*0.999 + 0.99*0.001 = 0.01098. Therefore, P(L/D) = 0.01*0.999/0.01098 ≅ 0.909836, as quoted above. Like a student, I'm quite happy to be able to "derive" this :-)
Though the notes 13 and 14 have appeared on p.59 (14th line) and p.60 (28th line) respectively, we see notes 13 and 14 again on p.69 (lines 13 and 28) and they should really be notes 15 and 16. And in fact, note 15 on p.71 (27th line), note 16 on p.72 (1st line) and note 17 on p.74 (8th line) should be note 17, note 18 and note 19 respectively.
The note 7 of Chapter 7 (p.148) saying: "In Figure 7.2, the normal distribution has mean 0 and spread 1, and the Cauchy distribution has mean and scale parameter 1." is quite puzzling. Because the mean (of the normal distribution) shown in Fig. 7.2 is 10, not 0 (and Cauchy distribution doesn't really have a well-defined mean … but probably more like a median). On p.150, lines 11-13 say "a 5-sigma event is the probability of getting a value five times larger than the mean.". I believe "five times" should probably be something like "five times the sigma" as a 5-sigma event should be the probability of getting a value 5 sigmas away from the mean. [ When I communicated the above typos/errors to the author, the author said that "five times" should be replaced with "five or more normal standard deviations". He's also told me a few other errors that I hadn't noticed:
i) p.93, line 10: Replace the words “symmetrical three-dimensional shape” by the words “Platonic solid”, so that it reads “ … since there is no Platonic solid with ten identical faces …”;
ii) p.133, line 11 from the bottom: Change “2000” to “2002”, so that it reads “… Nobel Prize in Economic Sciences in 2002 …”;
iii) p.218, lines 6-7 from the bottom: Change “half-billion” to “500 billion”, so that it reads “Now contemplate the fact that there are some 500 billion stars in our galaxy …”. ]...Continua