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Fifty Challenging Problems in Probability with Solutions (Dover Books on Mathematics) Paperback – May 1, 1987
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From the Back Cover
About the Author
Charles Frederick Mosteller ( 1916–2006) was one of the eminent statisticians of the 20th century. He was the founding chairman of Harvard's Statistics department. Dr. Mosteller wrote more than 50 books and more than 350 papers, with over 200 coauthors.
Frederick Mosteller: Harvard Man
Frederick Mosteller (1916–2006) founded Harvard University's Department of Statistics and served as its first chairman from 1957 until 1969 and again for several years in the 1970s. He was the author or co-author of more than 350 scholarly papers and more than 50 books, including one of the most popular books in his field, first published in 1965 and reprinted by Dover in 1987, Fifty Challenging Problems in Probability with Solutions.
Mosteller's work was wide-ranging: He used statistical analysis of written works to prove that James Madison was the author of several of the Federalist papers whose authorship was in dispute. With then–Harvard professor and later Senator Daniel P. Moynihan, he studied what would be the most effective way of helping students from impoverished families do better in school — their answer: to improve income levels rather than to simply spend on schools. Later, his analysis of the importance to learning of smaller class sizes buttressed the Clinton Administration's initiative to hire 100,000 teachers. And, as far back as the 1940s, Mosteller composed an early statistical analysis of baseball: After his team, the Boston Red Sox, lost the 1946 World Series, he demonstrated that luck plays an enhanced role in a short series, even for a strong team.
In the Author's Own Words:
"Though we often hear that data can speak for themselves, their voices can be soft and sly." — Frederick Mosteller
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Top Customer Reviews
Though I've worked through the problems a couple of times, I bought a replacement copy when my original was "permanently borrowed" from my desk at work.
Many solutions leave some small and other thoughtful "leaps" for the full details to be appreciated. At first this can be annoying, but once you "step it up", you can't help getting productively engaged.
This book takes off where I ended up. The first problem is a variation on the "reach into a bag" probability problem. (Q: You reach into a drawer with red socks and black socks, and the probability of drawing 2 red socks is P=0.5. What is the minimum number of both colored socks?)
You won't find the typical probability problems that can be quickly solved with basic combinatorial analysis or the Bernoulli Coefficient. You'll find variations and completely new worlds of probability. The explanations are thorough but succinct, and will arm you with a new skill set for solving such problems.
There's no other book like it on Amazon, and for $7...
Comparable to Huff's "How to Lie with Statistics" in its originality and straight-forwardness.
Some of the problems are classic, such as the problem of how many people would it take for the probability that at least two of them have the same birthday is greater than a half (I'll give this answer away: 23. But do you know why?) One of the dice problems actually recalls the history of the development of probability as a separate mathematical field -- problem #19, involving dice bets that Samuel Pepys asked Isaac Newton to figure out. Some of the problems are simply openers for entire vistas in probability - avoid problems #51 and #52 if you wish to not become enmeshed in concerns of random walks (remember that one of Einstein's earliest papers was on Brownian motion - a molecular random walk.) I used problem #25, which deal with "random chords on a circle", to explore this classic probability paradox - I've ended up with three different figures, all of which seem plausible! It gets deep to what one means by "random chord".
This book, though so thin, is inexhaustible in spawning disturbing questions about probability; even more useful is that there are questions for people at =any= level of knowledge of probability. Those who wish to think about "counting" problems (like those involving rolling dice, or pulling balls out of urns) will find those here. Those who have an interest in continuous probability will find problems which will interest them. And those old probability pros who ponder the essence of chance will find meat for some productive chewing.