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Conditional Epectation of Multinomial

  1. Dec 10, 2014 #1
    So I'm trying to find E(X1,X2|Xn) where X1,X2,.....Xn are the numbers of cell observations in a multinomial distribution.


    How do I even calculate this? I know it is not independent so I cannot split it.

    Does it have something to do with the fact that E(Xi)=nPi ?
     
  2. jcsd
  3. Dec 10, 2014 #2

    Stephen Tashi

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    Intuitively, we would expect the distribution of [itex](X1, X2| Xn = 6) [/itex] to be a multinomial distribution for 6 less objects with the cell probabilities for [itex] X1, X2,..X[n-1] [/itex] scaled by a factor so they sum to 1. I don't know what your notation [itex] E(X1,X2...[/itex] means. Are you asking about a vector of expectations?
     
  4. Dec 11, 2014 #3
    Interesting. Makes sense.

    Well, E(X1,X2) is just expectation of x1 and x2
     
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