  We examine the problem of estimating the expectation values of two
observables when we have a finite number of copies of an unknown qubit state.
Specifically we examine whether it is better to measure each of the observables
separately on different copies or to perform a joint measurement of the
observables on each copy. We find that joint measurements can sometimes provide
an advantage over separate measurements, but only if we make estimates of an
observable based solely on the results of measurements of that observable. If
we instead use both sets of results to estimate each observable then we find
that individual measurements will be better. Finally we consider estimating the
expectation values of three complementary observables for an unknown qubit.
