  It is shown that the exponential is the only distribution which satisfies a
certain regression equation. This characterization equation involves the
conditional expectation (regression function) of a record value given a pair of
record values, one previous and one future, as covariates. The underlying
distribution is exponential if and only if the above regression equals the
expected value of an appropriately defined Beta distributed random variable. In
a particular case, the expected value of the Beta variable reduces to a
weighted average of the covariates.
