I'm wondering about sampling without replacement until an object is found. I can't seem to wrap my head around it.
The random variable I want to use is X which I let bet the number of objects examined until the object is found. So I'm interested in the probability mass function here.
My attempts so far are:
(i) Take one sample at a time. Then each sample is a Bernoulli trial with probability at the k-th sample = 1/(n-k+1), 1 <= k <= n
So to get P(X=x) I multiply each 1/(n-k+1) from 1 to k inclusive? i.e. P(X=x) = 1/(n-k+1)!
(ii) The problem looks kind of like a hypergeometric distribution with parameters: number of draws = k, pop. size = n, contains 1 success
But the hypergeometric pmf is constructed in terms of obtaining some number of successes from a potential group of successes within the population. For my problem however there is only one success in the potential success group and we want to stop when we get a success. So it's styled more in the way of a geometric distribution. Again, the random variable for a geometric dist. is number of trials needed to get a success.
I'm confused anyway, if anyone could shed some light on this I'd be very grateful, thanks