According to the article "Reliability Evaluation of Hard Disk Drive Failures Based on Counting Processes" (Reliability Engr. and System Safety, 2013: 110-118), particles accumulating on a disk drive come from two sources, one external and the other internal. The article proposed a model in which the internal source contains a number of loose particles W having a Poisson distribution with mean value m; when a loose particle releases, it immediately enters the drive, and the release times are independent and identically distributed with cumulative distribution function G(t). Let X denote the number of loose particles not yet released at a particular time t. Show that X has a Poisson distribution with parameter m[1 - G(t)].