0
$\begingroup$

Suppose X is the number of heads in 10 tosses of a fair coin. Given X=5, what is the probability that the first head occurred in the third toss?

We can assume X to a Binomial distribution with p=1/2 and n=10. Let Y=number of trails required to get one success. I presumed Y can have a negative binomial distribution with r=1, that is a geometric distribution. But how do I incorporate the relation between X and Y?

This is not a homework question, but a question that has been asked in an entrance examination in the previous years.

Improve this question
$\endgroup$
10
  • $\begingroup$ Since it is given that the coin is fair, the parameter for Y should be 1/2. As I've studied in the Negative Binomial Distribution, the parameter r is taken as the number of success that we want and p is the parameter of the Bernoulli distribution. $\endgroup$
    – Nisha
    Commented Jun 24, 2020 at 7:00
  • $\begingroup$ By this reasoning, p=0.5 since the coin is fair $\endgroup$
    – Nisha
    Commented Jun 24, 2020 at 7:00
  • $\begingroup$ If we take y=3, this would mean that we are counting the probability of getting r=1 success in y=3 trials, where the probability of success is p=0.5 $\endgroup$
    – Nisha
    Commented Jun 24, 2020 at 7:02
  • $\begingroup$ I do not understand how to accommodate the relationship of the number of the successes in this i.e x=5 $\endgroup$
    – Nisha
    Commented Jun 24, 2020 at 7:03
  • $\begingroup$ Ah, actually I had missed the information that $X=5$. That changes things. Sorry. Please disregard my original comment, I'll delete it. $\endgroup$
    – Stephan Kolassa
    Commented Jun 24, 2020 at 7:11

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.