Conditional Epectation of Multinomial

[torquerotates]

Main Question or Discussion Point

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 ?

 

[Stephen Tashi]

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

 

[torquerotates]

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

Interesting. Makes sense.

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