Roseate spoonbills are common along I the Gulf Coast of the U.S. See nationalzoo.si.edu/Animals/Birds/Facts/fact-rosespoonbill.cfm for more information.

Question:

Roseate spoonbills are common along I the Gulf Coast of the U.S. See nationalzoo.si.edu/Animals/Birds/Facts/fact-rosespoonbill.cfm for more information. Suppose that the number of j roseate spoonbills that fly overhead in 1 hour (at a nature preserve) has a Poisson with mean 2. Also suppose that the number of roseate spoonbills is independent from hour to hour. For example, the number of birds between noon and 1 PM does not affect the number of birds between 1 PM and 2 PM.
a. A bird watcher sits and looks for the birds for 3 hours. How many of these birds does she expect to see?
b. What is the probability that she sees exactly 5 of these birds during a 3-hour time period?
c. What is the probability that she sees exactly 1 bird in each of 3 separate 1-hour time periods? Which is this, and what are the parameters?
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