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This paper studies the statistical properties of the signal-to-noise ratio (SNR) of the dual-hop relaying link in a cooperative wireless communication system in the presence of channel estimation errors for fixed-gain (FG) and variable-gain (VG) relays. The SNR expression is derived and three different analytical approaches with different simplifying assumptions are proposed to obtain the probability distribution function of the SNR and the outage probability in each mode. All but one approach result in closed-form expressions for the outage probability. The simplest approach in each mode has been used to find an optimum power allocation scheme for pilot and data symbols transmission at the source and the relay that results in minimizing the outage probability. Numerical analysis is used to confirm the accuracy of the derived theory and to show that the analytical approaches have a good outage performance, especially as the relay-destination distance increases. It is shown that significant power savings (e.g. 6 dB in VG mode) can be obtained by using the proposed power optimization method.