The discussion centers on calculating the conditional expectation E(X1, X2 | Xn) for a multinomial distribution, where X1, X2, ..., Xn represent the counts of observations in different categories. Participants confirm that E(Xi) equals nPi, where Pi is the probability of each category. The conditional distribution of (X1, X2 | Xn = 6) is identified as a multinomial distribution with adjusted probabilities for X1 and X2, scaled to ensure they sum to 1. Clarification is provided regarding the notation E(X1, X2), which refers to the expectation of the random variables X1 and X2.
PREREQUISITESStatisticians, data analysts, and anyone involved in probability theory or working with multinomial distributions will benefit from this discussion.
Stephen Tashi said: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?