Extra Problems

Example 1

Side note:

Example 2

Example 3

Example 4

Example 5 (from Dekking)

Example 4

Example 5 (from Dekking) For random variables X and Y shown in table below, E[XY] is computed as shown.

Example 6 (from Dekking) Suppose X and Y have the the following joint

…. Compute this (ans: 187/2025)

MARKOV AND CHEBYSHEV Example 7

Example 8

Example 9 (10.2 from Dekking) Consider two random variables X and Y with the following joint distribution

A. Determine E[XY] B. Are X and Y independent? Why? C. Are X and Y correlated? Why? D. Determine Var(X + Y). E. Determine Var(X - Y).

Solution:

Example 10 (10.3 from Dekking)

Solution:

Example 11.

Example 12.