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

Y1=0 if the child survived

=1 if not

Y2=0 if no belt used

=1 if adult belt used

=2 if car-seat belt is used

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

Y1

Y2 1 2

0 0.38 0.17 0.55

1 0.14 0.02 0.16

2 0.24 0.05 0.29

0.76 0.24 1

Are Y1 and Y2 independent? Why or why not?

Y1=0 if the child survived

=1 if not

Y2=0 if no belt used

=1 if adult belt used

=2 if car-seat belt is used

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

Y1

Y2 1 2

0 0.38 0.17 0.55

1 0.14 0.02 0.16

2 0.24 0.05 0.29

0.76 0.24 1

Are Y1 and Y2 independent? Why or why not?

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