This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1903 Excerpt: ...find the most probable value. That is the problem it is attempted to solve by the method of least squares. As a second question, it is required to determine the precision of the result, that is, to state the probability that it is correct within assigned limits. Before going further I must call attention to one very ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1903 Excerpt: ...find the most probable value. That is the problem it is attempted to solve by the method of least squares. As a second question, it is required to determine the precision of the result, that is, to state the probability that it is correct within assigned limits. Before going further I must call attention to one very important point in the reasoning. In the reasoning on which the method of least squares is based it is assumed that the frequency-curves are normal curves of error, as written above. If the frequency-curve is not a normal curve of error the method breaks down at the first step. That I shall have to return to later. With regard to the moduli, we may either suppose that we know them by some a priori method, as is sometimes the case; or that we know them by having made similar experiments at some other time, e.g., if we are dealing with a group of height measurements where the modulus is three inches generally; or we may find them from the experiments themselves. A useful way is to repeat the measurement by each method, say, 100 times, and from the internal evidence find out what the moduli are. We assume that the moduli are fixed quantities, quantities which we cannot affect, and that they are known or previously determined quantities. What is the probability that a certain series of errors should result in n observations? Let xx, .... xn be the differences from the unknown true value which arise from n different methods taken in one series; what is the probability that those particular n deviations will occur at once? The probability is obtained by multiplying together the probabilities of their separate occurrences. The probability of the error xx occurring, when the modulus is ch is from its curve of 1 frequency e r. The probability that the n w..
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Seller's Description:
91 pp, library markings, lower inside tips chipped with no loss, entirely disbound and lacks paper wrappers, reading copy only. -If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.