Probability Distribution of the Hubble Constant and the Age of the Universe Inferred from the Local Observation

We present a method to compute the probability distribution function of the (true) Hubble constant and the age of the universe, given the estimate of the Hubble constant in our nearby galaxy samples. Our method takes into account both the observational errors and the cosmic variance, and enables to quantitatively compute the constraints on the cosmological models. Based on the present local observation $H_0=80\pm 17$ km/s/Mpc, the probability of $H_0<50$ km/s/Mpc is about 6% for the Einstein – de Sitter universe (${\mathrm{\Omega }}_0=1$) and 4% for an open (${\mathrm{\Omega }}_0=0.2$) universe. These probabilities are reduced to 0.8% and 0.03%, respectively, if the accuracy of the observational uncertainty is improved within 10%. Similar probabilistic constraints on $t_0$ are also discussed.