You are building a full Bayesian network for a public-transit dataset. One discrete variable represents how many minutes a commuter waits for a bus; buses arrive every 10 minutes and the observed mean wait is 3 minutes. Which prior distribution is most appropriate for this discrete waiting-time variable?

The Poisson distribution is most appropriate because it models the number of events (bus arrivals) occurring within a fixed interval of time or space, given a known average rate. Here, the average wait time (3 minutes) is known, and the variable is discrete (minutes waited). The Uniform distribution is incorrect because it implies all outcomes within a range are equally likely, which is not the case for waiting times where shorter waits are generally more probable. The Normal distribution is incorrect as it is a continuous distribution and can produce negative values, which are not applicable for waiting times. The Binomial distribution is incorrect because it models the number of successes in a fixed number of independent Bernoulli trials, which doesn't fit the scenario of continuous waiting time.