Is it possible to find the $E[X_i | \sum_j X_j \geq c]$ where $c$ is a known constant and the $X_j$ are correlated random variables. $X_i$ is in the $X_j$ terms. I know the correlation matrix between the $X_j$ terms. I can also find the distribution of each of the $X_j$ terms.
Any help or suggestions on how to approach the problem would be greatly appreciated.
Its hard to tell how to calculate $E(X_i I(\sum_jX_j \geq c))$ if one doesn't know anything about the convolution distribution. In general one could go like this $$ \int_0^\infty x_i \int_{c-x_i}^\infty \,dP^{\sum_{j\neq i}X_j |X_i=x_i} \,P^{X_i}(dx_i) = \int_0^\infty x_i P(\sum_{j\neq i}X_j + x_i\geq c\,|\,X_i=x_i) \,P^{X_i}(dx_i) $$