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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


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    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!
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