1
$\begingroup$

Let $X$ be a random variable that represents the number of trials of a given experiment. The outcome of a single trial is a Bernoulli random variable, with probability of success $p$, and trials are independent.

The maximum number of trials is $n$, but if there are $k<n$ consecutive successes the experiment ends.

What is the probability distribution?

$\endgroup$

1 Answer 1

1
$\begingroup$

Let $a_n$ be the required probability.

Then $a_{n+1} = a_n+(1-a_{n-k})p^k(1-p)$

Where $a_0=a_1=a_2=...=a_{k-1}=0,a_k=p^k$

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .