18.5. Linearity of Expectation 783
Class Problems
Problem 18.21.
A classroom has sixteen desks in a 4 4 arrangement as shown below.
If there is a girl in front, behind, to the left, or to the right of a boy, then the two
flirt. One student may be in multiple flirting couples; for example, a student in a
corner of the classroom can flirt with up to two others, while a student in the center
can flirt with as many as four others. Suppose that desks are occupied mutually in-
dependently by boys and girls with equal probability. What is the expected number
of flirting couples?Hint:Linearity.
Problem 18.22.
Here are seven propositions:
x 1 OR x 3 OR x 7
x 5 OR x 6 OR x 7
x 2 OR x 4 OR x 6
x 4 OR x 5 OR x 7
x 3 OR x 5 OR x 8
x 9 OR x 8 OR x 2
x 3 OR x 9 OR x 4Note that:- Each proposition is the disjunction (OR) of three terms of the formxior the
formxi.