SOA Exam P Sample Question 606
Study guide: Exam P-1
Along a highway, automobiles are randomly selected for tire inspections. Let X denote the number of bad front tires and Y the number of bad rear tires on a randomly selected automobile. The joint distribution of X and Y is given by the probability function
p(x, y) = \begin{cases}
\dfrac{(6 - x)(3 - y)}{58\left(1 + |x - y|\right)}, & \text{for } x = 0, 1, 2 \text{ and } y = 0, 1, 2 \\[6pt]
0, & \text{otherwise.}
\end{cases}Calculate the variance of the number of bad front tires among those automobiles with one bad rear tire.
- A)
7/16 - B)
49/100 - C)
2/3 - D)
7/10 - E)
1
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