  There is a growing body of work on sorting and selection in models other than
the unit-cost comparison model. This work is the first treatment of a natural
stochastic variant of the problem where the cost of comparing two elements is a
random variable. Each cost is chosen independently and is known to the
algorithm. In particular we consider the following three models: each cost is
chosen uniformly in the range $[0,1]$, each cost is 0 with some probability $p$
and 1 otherwise, or each cost is 1 with probability $p$ and infinite otherwise.
We present lower and upper bounds (optimal in most cases) for these problems.
We obtain our upper bounds by carefully designing algorithms to ensure that the
costs incurred at various stages are independent and using properties of random
partial orders when appropriate.
