1. The problem statement, all variables and given/known data
A coin is flipped repeatedly with probability [tex]p[/tex] of landing on heads each flip.
Calculate the average [tex]<n>[/tex] and the variance [tex]\sigma^2 = <n^2> - <n>^2[/tex] of the attempt n at which heads appears for the first time.
2. Relevant equations
[tex]\sigma^2 = <n^2> - <n>^2[/tex]
3. The attempt at a solution
I have the probability that head will appear for the first time on the nth attempt to be [tex]p(1-p)^{n-1}[/tex]. Aside from that I'm not sure where to go.
A coin is flipped repeatedly with probability [tex]p[/tex] of landing on heads each flip.
Calculate the average [tex]<n>[/tex] and the variance [tex]\sigma^2 = <n^2> - <n>^2[/tex] of the attempt n at which heads appears for the first time.
2. Relevant equations
[tex]\sigma^2 = <n^2> - <n>^2[/tex]
3. The attempt at a solution
I have the probability that head will appear for the first time on the nth attempt to be [tex]p(1-p)^{n-1}[/tex]. Aside from that I'm not sure where to go.
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