Question
Let Xi denote the number of lead changes during the Daytona 500 NASCAR Cup Series race between 1959 and 2020. Suppose X 1959, ... ,
Let Xi denote the number of lead changes during the Daytona 500 NASCAR Cup Series race between 1959 and 2020. Suppose X 1959, ... , X2020 are iid samples from a Poisson(1) distribution. Also, assume a "vague" prior 1 ~ gamma(0.0001, 0.0001).
a) Describe why I ~ gamma(0.0001, 0.0001) is considered a "vague" prior.
b) Find the posterior distribution for lamda.
(c) Compute the posterior mean for lamda.
(d) Find and interpret a 95% equal-tail credible interval for lamda.
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Probability And Statistics
Authors: Morris H. DeGroot, Mark J. Schervish
4th Edition
9579701075, 321500466, 978-0176861117, 176861114, 978-0134995472, 978-0321500465
