(adsbygoogle = window.adsbygoogle || []).push({}); Statistics: geometric distribution "proof" problem

1. The problem statement, all variables and given/known data

IfYhas a geometric distribution with success probabilityp, show that:

P(Y = an odd integer) = [itex]\frac{p}{1-q^{2}}[/itex]

2. Relevant equations

p(y)=p(q)[itex]^{2}[/itex]

3. The attempt at a solution

p(1)=pq^0

p(3)=pq^2

p(5)=pq^4

.

.

p(2k+1)=pq^2k

I also know the sum of a geometric series is basically [itex]\frac{first-next}{1-ratio}[/itex]

Basically, I'm stuck on how to something set up so I can do some manipulation to eventually lead to P(Y = an odd integer) = [itex]\frac{p}{1-q^{2}}[/itex]

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# Statistics: geometric distribution proof problem

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