Mathematically,the probabilities P (X =1), P (X =2), P (X =3), ... form ageometric progression:eachprobabilityinthe sequence is a constant multiple (inthiscase1−p)ofthe precedingone.Thisisthe reason forthe name ‘geometric’. TheAncient Greek mathematicianEuclid knew about geometric progressions Moreover, since0
<1, it follows that 0 < 1 − p<1also, so each consecutive probabilityissmallerthanthe precedingone.Inother words, the geometric p.m.f.isalwaysadecreasing function of x
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