We consider the problem of learning the optimal action-value function in discounted-reward Markov decision processes (MDPs). We prove new PAC bounds on the sample-complexity of two well-known model-based reinforcement learning (RL) algorithms in the presence of a generative model of the MDP: value iteration and policy iteration. The first result indicates that for an MDP with $N$ state-action pairs and the discount factor γin[0, 1) only $O(N log(N/δ)/ [(1 - γ)3 \epsilon^2])$ state-transition samples are required to find an $\epsilon$-optimal estimation of the action-value function with the probability (w.p.) 1-δ. Further, we prove that, for small values of $\epsilon$, an order of $O(N log(N/δ)/ [(1 - γ)3 \epsilon^2])$ samples is required to find an $\epsilon$ -optimal policy w.p. 1-δ. We also prove a matching lower bound of $\Omega(N log(N/δ)/ [(1 - γ)3\epsilon2])$ on the sample complexity of estimating the optimal action-value function. To the best of our knowledge, this is the first minimax result on the sample complexity of RL: The upper bound matches the lower bound interms of $N$ , $\epsilon$, δ and 1/(1 -γ) up to a constant factor. Also, both our lower bound and upper bound improve on the state-of-the-art in terms of their dependence on 1/(1-γ).