Jump to content

  • Log In with Google      Sign In   
  • Create Account


ratio and number of samples


Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.

  • You cannot reply to this topic
2 replies to this topic

#1 lomateron   Members   -  Reputation: 302

Like
0Likes
Like

Posted 07 February 2014 - 02:40 AM

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?

 



Sponsor:

#2 Álvaro   Crossbones+   -  Reputation: 12003

Like
1Likes
Like

Posted 07 February 2014 - 03:18 AM

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?

#3 lomateron   Members   -  Reputation: 302

Like
0Likes
Like

Posted 07 February 2014 - 03:55 AM

no


Edited by lomateron, 07 February 2014 - 04:04 AM.





Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.



PARTNERS