After a break, we are back with a Bayesian problem. It is taken from the Penn State site and combines the Bayes rule with Poisson probabilities.
Amy thinks the average number of cars passing an intersection is 3 in a given period, whereas Becky thinks it’s 5. On a random day of data collection, they observed seven cars. What are the probabilities for each of their hypotheses?
Let’s give equal prior probabilities for both (P(lambda = 3) P(lambda = 5) = 0.5). P(X = 7 | lambda = 3) is given by the Poisson probability density function:
dpois(7, 3)
dpois(7, 5)0.022
0.105
