Conditional Epectation of Multinomial

  • #1

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 ?
 

Answers and Replies

  • #2
Stephen Tashi
Science Advisor
7,016
1,237
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?
 
  • #3
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?
Interesting. Makes sense.

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

Related Threads on Conditional Epectation of Multinomial

  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
4K
Replies
2
Views
2K
Replies
3
Views
392
Replies
6
Views
529
Replies
2
Views
3K
Replies
4
Views
352
Replies
3
Views
516
Top