Monday, May 29, 2006

Books (Math): Chance

I've been reading David Whitehouse's The Sun: A Biography, but on Friday I forgot to bring it to work. Stuck without anything to read, I dropped by the book store and picked up Chance: A Guide to Gambling, Love, The Stock Market, & Just About Everything else.

Chance is a rather slim book -- which was what I was after, something to tide me over until I got back to my copy of The Sun -- that covers a lot of the same ground as Struck By Lightning, though more it covers that ground more lightly (the chapter on game theory is all of one page long!).

The book is so slim, in fact, that each chapter feels like it's ending about halfway through. It's hard for me to tell if it actually has enough material to be a good introduction for someone unfamiliar with statistics -- it seems too thin to me. But it is well-written and accessible, so it may well be a good starting point for the subject.

My biggest problem with the book is actually with the typesetting -- specifically, the typesetting of equations. There are some serious gaffes. When talking about the Gambler's Ruin, the book presents this formula:

1 - (q/p)m
P = 1 - (q/p)m+n

Of course, what they actually mean is:

P =1 - (q/p)m
1 - (q/p)m+n

It's not so bad in this example, but in some cases it gets very hard to figure out just what's supposed to be equal to what.

Another example is in the chapter on statistical sampling. The formula for the standard deviation of the normal distribution is:

(sample proportion) × (-1 sample proportion)
sample size

Of course, the correct formula is:

(sample proportion) × (1 - sample proportion)
sample size

There's a big difference between (-1 sample proportion) and (1 - sample proportion)!

This isn't Aczel's fault (on the next page, when values for sample proportion and sample size are substituted in, the formula is correct), but it should have been caught before the book went to print.

In spite of the book's lightness and the typographic problems, it's still an enjoyable book. There was even a nice coincidence in the chapter on coincidences. Aczel mentions his friend Scott Petrack who, when flying from Paris to Boston, discovered that the person he'd been sitting beside had sung in the same choir in Tanglewood (the summer home of the Boston Symphony Orchestra) about twenty years before. A week later, Scott got a business call from a stranger, and discovered that that person had sung in the same Tanglewood choir.

As it turns out, my father was also a member of the Tanglewood Festival Chorus about twenty years ago. There's a good chance he sang with Scott Petrack and the other two people, and that I heard them all. Not bad for an example of coincidence.

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