Jump to content
  • Advertisement
Sign in to follow this  

ratio and number of samples

This topic is 2079 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Recommended Posts

I have a table full of heads

Each head took a test and the only thing I know about the test of each head are their results

The results show the total number of questions and the number of correct answers 

Each head has a different total number of questions

I have to select the most intelligent head


Q=total number of questions

A=correct answers


one head took only 1 question and got it correct, other head took 4 and 3 were correct, is second head more intelligent than first?


what can I do?


Share this post

Link to post
Share on other sites
Let's imagine each head has a true probability of getting a question right, but this probability is hidden to you. If you start with a prior that the probability is uniformly distributed between 0 and 1, after A correct answers and B incorrect answers the posterior distribution is a beta distribution with parameters alpha=A+1 and beta=B+1. Now we can easily compute the expected value of the hidden probability to be the mean of the posterior distribution, alpha/(alpha+beta) = (A+1)/(A+B+2).

So in your case, the first head gets a expected hidden probability of 2/3, while the other head's is 4/6, which is the same. However, looking at the mean only is a bit simplistic. The probability that the second head is more intelligent than the first head is actually 10/21 = .47619.

But of course, the answer would be different with a different prior distribution of hidden probabilities.

Is this homework?

Share this post

Link to post
Share on other sites
Sign in to follow this  

  • Advertisement

Important Information

By using GameDev.net, you agree to our community Guidelines, Terms of Use, and Privacy Policy.

GameDev.net is your game development community. Create an account for your GameDev Portfolio and participate in the largest developer community in the games industry.

Sign me up!