Download e-book for kindle: Teach Yourself Statistics by Richard Goodman

By Richard Goodman

ISBN-10: 0340059060

ISBN-13: 9780340059067

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The number of ways r objects may be arranged among themselves is clearly r\ (by the previous problem). Hence x = n\jr\(n — r)\ This number is usually denoted by the symbol nCr or by {^j. Example : In how many different orders can a row of coins be placed using 1 shilling, 1 sixpence, 1 penny and 6 halfpennies ? If we treat the halfpennies as all different the number of arrangements is 9 ! But it is possible to arrange the halfpennies in 6 ! different ways, all of which we now consider to be equivalent.

Thus /•wa B(m, n) = 2 / sin 2 ™- 1 ^ cos 2 "- 1 d . a useful alternative form. 5) C. Relation between Gamma and Beta Functions. It can be shown t h a t B(m, n) and T(w) and r(n) are related by the formula which immediately displays the symmetry of the B-function in m and n. I t follows that, since B(\, = tt and T(l) = 1 B(b i) = (T(i)) 2 or m 1 = Vk Abbott, op. , p. 225. 2) STATISTICAL MODELS. 3), we have r(-J-) = 2 J exp ( - x2)dx. Consequently / 00 exp (—x*)dx = . . 3) a result we shall need later.

The distribution is not, for example, J-shaped) the calculated first moment need not be corrected, b u t the calculated variance should be reduced by an amount equal to h*/12, where h is the length of each class-interval. If, however, h is less t h a n one-third of the calculated s t a n d a r d deviation, this a d j u s t m e n t makes a difference of less t h a n in the estimate of the s t a n d a r d deviation. If the variate is essentially discrete, Sheppard's correction should not be applied (see Aitken, Statistical Mathematics, pp.

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Teach Yourself Statistics by Richard Goodman

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