The Mutual Information Principle (MIP) was proposed as a method of inferring the pdf of a continuous random variable based on discrete observations. Its main disadvantage has been the unavailability of closed form solutions. The purpose of this paper is to present some new, easily obtainable closed form solutions, which are based on a new result in Rate Distortion Theory (RDT). The solutions shed new light on the workings of the MIP, but are not unique. This lack of uniqueness is explained and its effects are discussed.
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