The average outage probabilities of the amplify-and-forward (AF) relaying and the decode-and-forward (DF) relaying with/without diversity in Rayleigh fading were analyzed respectively, and the analytical expressions were presented. To minimize the average outage probability, with total transmit power constraint, the statistically optimal power allocation problem of the AF relaying and DF relaying were considered, and also the analytical expressions are provided. Then the statistical optimal relay selection was suggested to further minimize the average outage probability. Though the analytical expressions of power allocation for AF and DF with diversity were obtained under the condition of high transmit SNR, the simulation results show that they are also valid in the low transmit SNR region. Compared with fixed power allocation, the statistical optimal power allocation effectively reduces the average outage probability. Meanwhile, the optimal relay selection further reduces the average outage probability.