Help proving and finding Geometric Distribution. The Geometric Distribution : As

Question

Help proving and finding Geometric Distribution.

The Geometric Distribution : Assume that the probability of success of one experiment is p (sometime small, but not necessarily) and the probability of failure is 1-p . we wish to perform this experiment until we gat one success. Justify the statement that the probability that it taken n trials for one success is given by P(n) =(1-p)n-1 p. (we choose the same letter for the function as the probability of success because everyone else does. Unfortunate, I know.) Prove that p(n)= 1. Find np(n). Find n2p(n) . Find ( n2p(n)) -( np (n))2.

Explanation / Answer

(b) series = p + (1-p)p + (1-p)^2*p + (1-p)^3*p + ...............

series = p[ 1/(1-1+p) ] = p*(1/p) = 1

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