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January 26th, 2017, 05:59 PM   #1
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Odds and Distributions

I'll preface by saying, this might not make any mathematical sense, which is why I'm here. When I learn, I like to relate new material to existing knowledge and I want to know if this makes sense before I encode it.

a geometric distribution has the f(n): P*(1-P)^n-1 where p is probability of success and n is #of times event occurs

a binomial distribution has the f(n): P^(x)(1-P)^(n-x)

The odds of an event occurring are: P/(1-P)

What I am curious about is whether there exists a relationship between binomial and odds or geometric and odds.

Furthermore, If I were to take the E(exp{tY}) where Y is my odds. would there be an MGF for odds and therefore an odds distribution?

or is this a silly/flawed way to look at these?
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January 26th, 2017, 08:19 PM   #2
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Nope, unfortunately. You should look at the definition of a random variable. The odds of getting a particular outcome is deterministic, rather than a random variable, so I'm afraid there's no MGF there.
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