[Steps Shown] X and Y are i.i.d. random variables with common probability mass function Pr (X=k)=Pr (Y=k)=pq^k, k=0,1,2,3,... Define Z = minX,Y. Find the probability


Question: X and Y are i.i.d. random variables with common probability mass function

\(\Pr \left( X=k \right)=\Pr \left( Y=k \right)=p{{q}^{k}},\,\,\,k=0,1,2,3,...\)

Define Z = min{X,Y}. Find the probability mass function of Z.

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