  We study four problems namely, Campbell's source coding problem, Arikan's
guessing problem, Huieihel et al.'s memoryless guessing problem, and Bunte and
Lapidoth's task partitioning problem. We observe a close relationship among
these problems. In all these problems, the objective is to minimize moments of
some functions of random variables, and R\'enyi entropy and Sundaresan's
divergence arise as optimal solutions. This motivates us to establish a
connection among these four problems. In this paper, we study a more general
problem and show that R\'{e}nyi and Shannon entropies arise as its solution. We
show that the problems on source coding, guessing and task partitioning are
particular instances of this general optimization problem, and derive the lower
bounds using this framework. We also refine some known results and present new
results for mismatched version of these problems using a unified approach. We
strongly feel that this generalization would, in addition to help in
understanding the similarities and distinctiveness of these problems, also help
to solve any new problem that falls in this framework.
