2017 October 20,

Math 265: Day 17

Carleton College, Prof. Joshua R. Davis

Due at the start of class on Day 22

Complete these problems. Write them up carefully, in the order assigned, for handing in with the rest of your homework.

The first two problems below concern the joint distribution example from class, in which f(x, y) = (1 - x² - y²) * 2 / π on the unit disk.

• Compute the marginal distributions f_X(x) and f_Y(y) (defined on page 241 of our textbook). Be clear about their domains of definition (outside of which they are assumed to be 0).
• Give an example of a function g(X, Y), and compute the expectation E[g(X, Y)] for it (as defined on page 242). Your example should not be trivial, but nor should it be so complicated that you can't compute the expectation.
• 6.30, 6.31
• 6.38