  We consider the transmission of a memoryless bivariate Gaussian source over
an average-power-constrained one-to-two Gaussian broadcast channel. The
transmitter observes the source and describes it to the two receivers by means
of an average-power-constrained signal. Each receiver observes the transmitted
signal corrupted by a different additive white Gaussian noise and wishes to
estimate the source component intended for it. That is, Receiver~1 wishes to
estimate the first source component and Receiver~2 wishes to estimate the
second source component. Our interest is in the pairs of expected squared-error
distortions that are simultaneously achievable at the two receivers.
  We prove that an uncoded transmission scheme that sends a linear combination
of the source components achieves the optimal power-versus-distortion trade-off
whenever the signal-to-noise ratio is below a certain threshold. The threshold
is a function of the source correlation and the distortion at the receiver with
the weaker noise.
