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In this paper, we consider the problem of transmitting a Bi-variate Gaussian source S = (S1, S2) over an average-power-limited additive White Gaussian noise (AWGN) channel. The receiver wants to estimate both S1 and S2. We propose a new Hybrid Digital Analog (HDA) joint source-channel coding scheme and obtain its achievable distortion region. For comparison, we also obtain an outer bound for the set of all achievable distortion pairs.