I have a problem where i am uncertain how to set up a likelihood function
The number of tries before the first success follows a geometric distribution.
In a sample (n=100, iid) a mean number of tries was found to be 7.
So normally without the additional information setting the max. likelihood up as normal.
But now, as i only that that the mean number of tries was seven, not the actual 100 outcomes, can i say that
But solving this i get a negative estimator for p, which doesn’t ring true....
It seems logical to incorporate as much information as possible into my maximum likelihood estimate....
Or could it be possible that i don’t have to integrate the information because there is a point b, (a confidence Intervall) where i would need the mean of x.