Chapter 5.4, Problem 48E

In Exercise 5.4, you were given the following joint probability function for

$Y_1=\{\begin{array}{l}0,\text{ if child survived,}\\ 1,\text{ if not,}\end{array}\text{ and }{Y}_2=\{\begin{array}{l}0,\text{ if no belt used,}\\ 1,\text{ if adult belt used,}\\ \text{2, if car-seat belt used}\text{.}\end{array}$

Are Y₁ and Y₂ independent? Why or why not?

5.4 Given here is the joint probability function associated with data obtained in a study of automobile accidents in which a child (under age 5 years) was in the car and at least one fatality occurred. Specifically, the study focused on whether or not the child survived and what type of seatbelt (if any) he or she used. Define

$Y_1=\{\begin{array}{l}0,\text{ if child survived,}\\ 1,\text{ if not,}\end{array}\text{ and }{Y}_2=\{\begin{array}{l}0,\text{ if no belt used,}\\ 1,\text{ if adult belt used,}\\ \text{2, if car-seat belt used}\text{.}\end{array}$

Notice that Y₁ is the number of fatalities per child and. since children’s car seats usually utilize two belts, Y₂ is the number of seatbelts in use at the time of the accident.

1. a Verify that the preceding probability function satisfies Theorem 5.1.
2. b Find F(1, 2). What is the interpretation of this value?