A forester studying diseased pine trees models the number of diseased trees per acre, Y , as a Poisson random variable with mean . However, changes from area to area, and its random behavior is modeled by a gamma distribution. That is, for some integer , f () = 1 () 1 e/ , > 0, 0, elsewhere. Find the unconditional probability distribution for Y .

ST 260 Chapter 5 Note. Part 1 – 2/10/14 Prof. Cali Davis Quick Recall: Quantitative Variables: differences that have meaning to them, such as age, income, height, and weight. Qualitative Variable (OR categorical): putting people or things into classifications. Such as: gender, race, occupation, country,...