# Download PDF by Banesh Hoffmann: About Vectors

By Banesh Hoffmann

ISBN-10: 0486604896

ISBN-13: 9780486604893

No calculus wanted, yet this isn't an straightforward ebook. Introduces vectors, algebraic notation and simple rules, vector algebra and scalars. Covers parts of parallelograms, triple items, moments, angular speed, parts and vectorial addition, extra concludes with dialogue of tensors. 386 routines.

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The size of the total sam pIe and the number sampled from each stratum will depend on the allocation method used. Three of the more common allocatlon methods used are described below. , nhln=N"IN. (ii) OPTIMUM ALLOCATION The sampie is allocated to the strata so that the variance of the estimator is aminimum, subject to the condition that the total budget available to cover the variable costs is fixed and equal to C and that the cost of sampling one unit in stratum h is C". i[N. ~ = N"S"I vC;: n h=l S"YC;] 44 (iii) Basic Statistics NEYMAN ALLOCATION The sampIe is allocated to the strata so that the variance of the estimator is aminimum, subject to the condition that the total budget available to cover the variable costs is fixed and equal to C and that the cost of sampling one unit is approximately the same in each strata.

Unbiased Estimator An estimator W of an unknown parameter X is unbiased if E (W) = E (X) for all values of x. Consistency Tbe estimator W is said to be consistent if the probability that W differs from X by more tban an arbitrary constant c approacbes zero when n-> 00; lim P (IW-XJI>c)-+O. In other words, the n--'>-oo probability of a large error goes to zero for large n. Sufficient conditions for consistency of Ware, that W is unbiased and var W--'>-O when n--'>- 00 . RELATIVE EFFICIENCY The relative efficiency of two estimators W 1 and W 2 can be measured by the ratio of their variances : (var W l ) !

ALLOCATlON OF SAMPLE In stratified random sampling, the total sampIe n may be allocated to the variöus strata in a number of ways. The size of the total sam pIe and the number sampled from each stratum will depend on the allocation method used. Three of the more common allocatlon methods used are described below. , nhln=N"IN. (ii) OPTIMUM ALLOCATION The sampie is allocated to the strata so that the variance of the estimator is aminimum, subject to the condition that the total budget available to cover the variable costs is fixed and equal to C and that the cost of sampling one unit in stratum h is C".

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