1. Airfreight Breakage. A substance used in biological and medical research is shipped by air freight to users in cartons of 5,000 ampules. The data below, involving ten shipments, were collected on the number of times a carton was transferred from one aircraft to another over the shipment route (X) and the number of ampules found to be broken upon arrival (Y). XNA10203101202 Y18169171222138151911NA (a) Fit Y by Poisson regression, with X as a covariate. Report the deviance of your t. Use noninformative priors. (b) According to your model, how many packages on average are expected will be broken if the number of shipment routes is X = 4? What is 95% CS for your estimate. (c) For a particular package sent from Shenzhen you learned that a shipment would involve X : 4 shipping routes. Predict the number of broken packages. What is here different from (b)? (d) What are estimates for unobserved X1 and 1/12? Hint. Note that for missing X, you need to specify the distribution. It could be any nonnegative valued distribution, but since X is discrete, a good choice is Poisson(2), as in forCi in 1:11)\"; vii-I "' dun-19(9)}