Abstract
Some formulas are provided for the absorption probabilities, the mean absorption times and the variances of 1st absorption times in finite homogeneous absorbing birth-death processes. The results are then applied to a genetic model of Moran for computing the absorption probability densities, the mean absorption times and the variances of 1st absorption times. The probability distribution of the 1st absorption time is the matrix analog of exponential distribution or a mixture of exponential distributions if the transition matrix is diagonal.