The History of Mathematics: A Brief Course

522 18. PROBABILITY AND STATISTICS standard deviation. This work brought the normal distribution into a more or less standard fo ...

PROBABILITY 523 the probability of its doing so were really only 50% because there are precisely two possible outcomes, most o ...

524 18. PROBABILITY AND STATISTICS is called the transition matrix. If successive transitions are all independent of one another ...

STATISTICS 525 useful. An early example was an argument intended to prove that the world was designed for human habitation bas ...

526 18. PROBABILITY AND STATISTICS at a higher temperature have molecules with higher kinetic energy—they are either more massiv ...

STATISTICS 527 involves an abandonment of strict dynamical principles and an adoption of the mathematical methods belonging to ...

(^528) 18. PROBABILITY AND STATISTICS Statistics has been the focus of metaphysical debate, just like mathematics. For some earl ...

STATISTICS 529 leave this topic without at least mentioning one of the giants in this area, Karl Pearson (1856-1936), a Britis ...

530 18. PROBABILITY AND STATISTICS FIGURE 3. Comparison of the chi-square distribution and the fre- quencies for the sum of the ...

QUESTIONS AND PROBLEMS 531 hiding itself very well. The curious reader is referred to Problem 18.7, where the paradox is explain ...

532 18. PROBABILITY AND STATISTICS represents the integral í/2ð Jo dt, which is the area under a standard normal (bell-shaped) c ...

QUESTIONS AND PROBLEMS 533 Put in the given values of ñ and iV 0 to compute the fraction of the initial sample that constitutes ...

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Chapter 19. Logic and Set Theory Logic has been an important part of western mathematics since the time of Plato. It also has a ...

536 19. LOGIC AND SET THEORY arithmeticians and algebraists, for whom inference consists only in the use of characters, and a mi ...

LOGIC 537 When we wish to give the idea of symbolical algebra... we ask, firstly, what symbols shall be used (without any refe ...

538 19. LOGIC AND SET THEORY De Morgan's notation in this work was not the best, and very little of it has caught on. He used a ...

LOGIC 539 altogether, and consider the word as meaning the state of the mind with respect to an assertion, a coming event, or ...

540 19. LOGIC AND SET THEORY properties of number, under another that of a geometrical problem, and under a third that of optics ...

LOGIC^541 The idea of probability 0 as indicating impossibility and probability 1 as indi- cating certainty must have had some ...