Let X; denote the number of lead changes during the Daytona 500 NASCAR Cup Series race between 1959 and 2020. Suppose X1959, . . . , X2020 are iid samples from a Poisson(lamda) distribution. Also, assume a prior lamda ~ gamma(ao, bo) and let x = (X1959, ..., X2020).

a) Set ao = bo = 0.0001 and compute the posterior predictive mean for X2021

b) Find and interpret a 95% equal-tail predictive interval for X2021 using ao = bo = 0.0001.

c) Test the hypothesis Ho : 1 > 25 vs. H:/< 25 using ao = bo = 0.0001