Stephen Tashi said: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?
Conditional expectation of multinomial is a statistical concept that refers to the expected number of successes in a multinomial experiment given certain conditions or events. It is used to predict the outcomes of a multinomial experiment based on prior knowledge or information.
The conditional expectation of multinomial is calculated by taking the product of each possible outcome with its corresponding probability, and then summing these products. This can be represented mathematically as E[X|A] = ∑x P(X=x|A), where X is the random variable, A is the event, and P(X=x|A) is the probability of X being equal to x given event A.
The unconditional expectation of multinomial refers to the expected number of successes in a multinomial experiment without any prior knowledge or information, while the conditional expectation of multinomial takes into account certain conditions or events and predicts the expected number of successes accordingly.
The conditional expectation of multinomial has various applications in real life, such as in market research, where it can be used to predict the success of a product based on certain demographics or characteristics of the target market. It is also used in sports analytics to predict the outcome of a game given certain conditions, such as player injuries or weather conditions.
The conditional expectation of multinomial is often used in decision-making processes to help weigh different options and make informed decisions. By taking into account certain conditions or events, it can provide a more accurate prediction of the expected outcomes, helping individuals or organizations make better decisions.