Section 8 Problem Types

A categorization of the 40 problems in Section 8 according to type. All of these problems involve bivariate and trivariate distributions.

1. Calculate unconditional probabilities for bivariate distributions where the:
    inequality involves both variables
       1, 2, 5, 10, 13, 18, 25, 28, 33.
    inequality involves only one of the variables
       3, 9, 14, 24, 27, 40.

2. Calculate unconditional probabilities for bivariate distributions:
    8, 15, 19, 31 (discrete).

3. Find marginal and conditional densities and probability functions.
    12, 36 (discrete).

4. Independence of random variables.
    4, 16, 22.

5. Find expectations, variances, and covariances of functions of random variables.
    7 (discrete), 11, 16, 23, 26, 29, 30, 32, 37, 38, 39.

6. Find conditional expectations and variances.
    6 (discrete), 7 (discrete), 17 (discrete), 20, 34 (discrete).

7. Moment-generating functions.
    22, 23.

8. Calculate probabilities and expectations by conditioning.
    1.

9. Bivariate Normal Distribution.
    21 (a fake).

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