1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Can someone Please help me understand E(X) expected values in statistics

  1. May 28, 2008 #1
    1. The problem statement, all variables and given/known data
    I have two dice, let X and Y denote (rspectively) min and maximum of the number of spots showing on the two die. Determine E(Y|X=x) for 1 <= x <=6.

    2. Relevant equations

    Basically all I need to do is work out E(Y| x=1), E(Y|x=2) and so on until x=6. The reason I am stuck is that the teacher has told me that E(Y|X=1)=1 and I don't understand how.

    3. The attempt at a solution

    I was thinking that E(Y|X=2) so that means (I think) that when X=2 that is the maximum, so then I thought Y could either be 1 or 2, so that means 2/36 ? But how come E(Y|X=1) is =1?

    See the problem is, statistics is the only branch of mathematics I don't enjoy so I can't really get my head around the question and what it's asking
  2. jcsd
  3. May 28, 2008 #2
    I don't understand what you mean by the "min and maximum of the number of spots showing on two die". A die has a fixed number of spots so how can there be a minimum and maximum?
  4. May 28, 2008 #3


    User Avatar
    Science Advisor
    Homework Helper

    Do you mean to say that X is the maximum and Y is the minimum? Because it does not make any sense that E(Y|X=1) = 1 otherwise.

    Suppose that that's what you mean. Then X = 1 implies Max{Die1,Die2} = 1. Clearly this is only possible in the case where Die1 and Die2 are both equal to 1, hence E(Y|X=1) = 1, as it's the only value Y can have.
  5. May 28, 2008 #4
    Think of it like this. You roll one die. It comes up, say, 4. Then you roll a 4-sided die. What's your expected value now? This is how conditional expectation works. So, E[Min | Max=4] = 1/4*(1+2+3+4) = 2.5.
  6. Dec 2, 2010 #5
    Say you have two die [tex]D_1[/tex] and [tex]D_2[/tex]. If one of them comes up as 1 and the other comes up as [tex]n[/tex] then [tex]min{D_1,D_2}[/tex] is always going to be 1. This is because the minimum of 1 and any other number has to be 1 because you can't roll lower than 1!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook