Packet sets and inverse packet sets are two kinds of novel mathematical tools to analyze dynamic information systems. With advances in inverse packet sets, random inverse packet information is proposed by introducing random characteristics into inverse packet sets. Hence, random inverse packet information has dynamic and random characteristics, and is an extended form of inverse packet sets. Furthermore, random feature, dynamic feature, and identification relation about the random inverse packet information are discussed. Finally, based on the above theory, an instance is used to illustrate the applications of intelligent acquisition of investment information.