I was watching the harvard stat110 course on Geometric distribution and the PMF is P(X=k)=pq^k where p is the probability of success and q=1-p. later he mentions another r.v Y which he defined as the 1st success distribution and he mentions that this distribution, unlike the Geometric Distribution, includes the first success.
Conrad Beltran
Answered question
2022-09-19
I was watching the harvard stat110 course on Geometric distribution and the PMF is where p is the probability of success and . later he mentions another r.v Y which he defined as the 1st success distribution and he mentions that this distribution, unlike the Geometric Distribution, includes the first success.
I got a bit confused as to the meaning of including the first success, in the PMF of Geo(p) there is a p, isn't this including the first success already?
Answer & Explanation
Rayna Aguilar
Beginner2022-09-20Added 14 answers
Imagine we have a sequence of Bernoulli trials (specifically, imagine we're tossing a biased coin).
I'm interested in Y, the number of trials to get the first head (how many tosses did I make to get a head), so let's call "got a head" a success, and it's the number of trials to get the first success. If I toss T, T, H, I count 3 trials.
My sister is interested in the number of times I failed to get a head before I succeeded, X (i.e. she only cares how many tails I got). If I toss T, T, H she counts "two failures".
Step 2
Both these variables are called "geometric" and the only difference is that my variable counts the trial on which I got a success in the total while my sisters variable does not (i.e. )
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