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correlation coefficient of two factors causing car accident

The total population of car passengers involved in traffic accidents are classified into six categories: two factors (one with 2 levels and one with 3 levels) crossed. The first factor is: Survivors (X1=0), Fatalities (X1=1). The second factor is: No Belt (X2=0), Adult Belt (X2=1), and Child Seat (X2=2). The proportions are as follow:

X1 = 0 X1 = 1
X2=0 | 0.38 | 0.17
X2=1 | 0.14 | 0.02
X2=2 | 0.24 | 0.05

a) Find E(X1), V(X1), E(X2), and V(X2)
b) Find cov(X1,X2)
c) Find the correlation coefficient between X1 and X2. How would you interpret the result?

Solution Summary

The solution shows how to calculate the covariance and the correlation coefficient of the two factors causing car accident.