The geometric distribution is:

Pr(X=k) = (1-p)k-1p for k = 1, 2 , 3 ...

A geometric series is a+ ar+ ar2, ... or ar+ ar2, ...

Now the sum of all probability values of k = Pr(X=1) + Pr(X = 2) + Pr(X = 3) ...

= p + p2+p3 ... is a geometric series with a = 1 and the value 1 subtracted from the series.

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M I K A E L M I K A E L M I K A E L

If the value given in the table for Z = z is k: that is, pr(Z > z) is 1 - k, then the two-tailed probability of observing a value which is at least as extreme, ie Pr(|Z| > z) is 0.5*(1-k).

Ginger fox Gnu J J K K Jpuljji K L L L

K. L. Dhammajoti was born in 1949.