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 ()) distribution. Also, assume a prior A ~ gamma(ao, bo) and let ac = (X1959, . . ., X2020). (a) (1 pt) Find the posterior predictive distribution for the number of lead changes for the 2021 Daytona 500, X2021 . That is, find P(X2,21 = x* (X = x). ep - (b) (1 pt) Find an expression for E( X2021 |a). edu ic