1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Probably easy expected value problem

  1. Mar 20, 2007 #1
    Hello, just a bit insecure about my answer.

    Suppose n people have throat cultures, and the cultures are then completely
    mixed up. If we randomly pair off the n peoples’ names with the n cultures,
    what is the expected number of correct labels?

    So, here's my logic on the solution:

    I think there are 2 random variables here, X1 for names, X2 for the cultures.
    The formula for the expected value for 2 random variables is:

    [tex]\sum_1^n \sum_1^n h(X1,X2)*prob(X1,X2)[/tex] for some weight function h.

    I chose h(X1,X2) = 1. Also, I said prob(X1,X2) = (1/n^2). I hope all that is right so far. So just using the expected value equation, I simply said the answer is 1.

    [tex]\sum_1^n \sum_1^n (1)* \left \frac{1}{n^2} \right = 1[/tex]

    Correct thinking? If not, what am I doing wrong?

    Thanks in advance,

    Last edited: Mar 20, 2007
  2. jcsd
  3. Mar 20, 2007 #2
    N labels on N bottles.

    1/N chance for label i to correspond to bottle i.

    Average number of correct labels= sum_i=1,N * chance for label i

    So I agree.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Probably easy expected value problem