An O(N) algorithm for computing expectation of N-dimensional truncated multi-variate normal distribution I: fundamentals

J. Huang was supported by the NSF grant DMS1821093, and the work was finished while he was a visiting professor at the King Abdullah University of Science and Technology, National Center for Theoretical Sciences (NCTS) in Taiwan, Mathematical Center for Interdisciplinary Research of Soochow University, and Institute for Mathematical Sciences of the National University of Singapore.