Probability and Theory of Errors
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Probability and Theory of Errors

Probability and Theory of Errors


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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. 1896 Excerpt: ...--1/2 + 2/5 = 9/10" t =-. 1/5. The determination of the law of error for this case presents some novelty, since it is essential to combine the continuous errors (1--t)et and tet with the discontinuous error e, . The simplest mode of attacking the problem seems to be the following quasi-geometrical one. In the notation of Arts. 12 and 13, put in (4) e = e, (1--t)e = e, tet = e and e, = e, . Then e = (e, + O + e, . (5) The law of error for (e, 4-ea) is given by equation (2) for any value of /. Hence for a given value of t there will be as many expressions of 0(e) as there are different values of e, . The graphs of 0(e) will all be of the same form but will be differently placed with reference to the axis of 0(e). Thus, if t = 1/3 the values of es are--1/3, o, and-4-1/3, and these are equally likely to occur. For e, = o the graph is given directly by (2), and is the trapezoid ABCD symmetrical with respect to OQ. For es =--1/3 the graph is abQd, of the same form as ABCD but shifted to the left by the amount of e, =--1/3. Similarly, the graph for the case of e, = 4-1/3 is a'Qb'd', and. is produced by shifting ABCD to the right by an amount equal to-4-1/3. Now, since the three systems of errors for this case are equally likely to occur, they may be combined into one system by simple addition of the corresponding element areas of the several graphs. Inspection of the diagram shows that the resultant law of error is expressed by 0(e) = (i/4)(5 4-6e) for-5/6 --1/6, j = 1 for--1/6 e + 1/6, i-(6) = (1/4X5-6e) for + 1/6 e + 5/6. J This is represented by a trapezoid whose lower base is 10/6, upper base 2/6, and altitude 1. Sum the three areas and divide by 3 to make resultant area = I, as required by equation (3), Art. 10. As a second illustration, conside...


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Product Details
  • ISBN-13: 9781154652789
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 24
  • Spine Width: 1 mm
  • Width: 189 mm
  • ISBN-10: 1154652785
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 64 gr


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