The table below shows the joint probability function of a sailor’s number of boating accidents and number of hospitalizations from these accidents this year.

	Number of Hospitalizations from Accidents
Number of Accidents		0	1	2	3
	0	0.700
	1	0.150	0.050
	2	0.060	0.020	0.010
	3	0.005	0.002	0.002	0.001

Calculate the sailor’s expected number of hospitalizations from boating accidents this year.

• 0.085
• 0.099
• 0.410
• 1.000
• 1.500

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: B

The marginal distribution for the probability of a given number of hospitalizations can be calculated by adding the columns. Then p(0) = 0.915, p(1) = 0.072, p(2) = 0.012, and p(3) = 0.001. The expected value is

0.915(0) + 0.072(1) + 0.012(2) + 0.001(3) = 0.099.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.