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For an arbitrarily-located user terminal (UE) in a multi-tier heterogeneous cellular wireless network, the joint distribution of the downlink SINR at the UE from the candidate serving base stations (BSs) in the accessible tiers of the network has been derived in closed form for the cases where the candidate serving BS from each accessible tier is chosen as either the one nearest to the UE  or the one that is received strongest (equivalently, with maximum SINR) at the UE , when the locations of the BSs in the tiers are modeled by independent Poisson Point Processes, and the fading on all links is assumed independent identically distributed (iid) and Rayleigh. The actual serving BS for the UE is chosen as the nearest/strongest/max-SINR candidate serving BS after imposing selection bias across the tiers. The above joint distributions can be used to yield the distribution of the actual SINR at the UE (i.e., when receiving from this serving BS) when no selection bias exists across tiers. However, for the practically important case of selection bias, analytical calculation of the distribution of the actual SINR presents significant challenges. This work derives and summarizes the distribution of actual downlink SINR for all the above criteria for selection of the serving BS accounting for selection bias. We then explore some implications of these results for design and operation of a heterogeneous network.