Given here is the joint probability function associated

QUESTION:

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}=\left\{\begin{array}{ll}

0, & \text { if the child survived, } \\

1, & \text { if not, }

\end{array} \text { and } Y_{2}=\left\{\begin{array}{ll}

0, & \text { if no belt used, } \\

1, & \text { if adult belt used, } \\

2, & \text { if car-seat belt used. }

\end{array}\right.\right.

\)

Notice that \(Y_{1}\) is the number of fatalities per child and, since children’s car seats usually utilize two belts, \(\(Y_{2}\)\) is the number of seatbelts in use at the time of the accident.

a Verify that the preceding probability function satisfies Theorem 5.1.

b Find \(F(1,2)\). What is the interpretation of this value?

Equation Transcription:

Text Transcription:

y_1=

0, if the child survived,

1, if not,

and  y_2=

0, if no belt used,

1, of adult belt used,

2, if car-seat belt used.

Y_1

Y_2

y_1

y_2

F(1,2)