A1 Summation And Product Operators

The Greek capital letter J2 (sigma) is used to indicate summation. Thus,

Some of the important properties of the summation operator are

1. Y^i=kk = nk, where k is constant. Thus, J]j4=1 3 = 4 ■ 3 = 12.

3. J2 n=1(a + bxi) = na + bYTi=\ X, where a and b are constants and where use is made of properties 1 and 2 above.

The summation operator can also be extended to multiple sums. Thus, Y, J2, the double summation operator, is defined as n m n mm Xij = (X1 + X2 +-----+ Xim)

870 APPENDIX A: A REVIEW OF SOME STATISTICAL CONCEPTS

Some of the properties of YJ2 are

1. IX i H j=i xij — E m—1 Hi—1 xij; that is, the order in which the double summation is performed is interchangeable.

3. Ei— 1T?= 1(xij+ yij) — Yi—^U*, + Ei— 1Y?— 1 yij.

4. [Hi—1 xi] — Hi — 1 Xi2 + 2 Hi = 1 Hi —i + 1 XiXj — Hi — 1 Xi2 + 2 Hi<, •

The product operator U is defined as n

Thus,

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