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0.2(1) + 0.8(8) = 6.6. | 0.2(1) + 0.8(8) = 6.6. | ||
{{soacopyright | 2023}} | {{soacopyright | 2023}} | ||
Latest revision as of 23:52, 5 May 2023
Solution: D
[math]X[/math] follows a geometric distribution with [math]p = \frac{1}{6}[/math]. [math]Y = 2[/math] implies the first roll is not a 6 and the second roll is a 6. This means a 5 is obtained or the first time on the first roll (probability = 20%) or a 5 is obtained for the first time on the third or later roll (probability = 80%).
[[math]]
\operatorname{E}[X | X \geq 3] = \frac{1}{p} + 2 = 6 + 2 = 8,
[[/math]]
so [math]\operatorname{E}[X | Y = 2] [/math] equals
0.2(1) + 0.8(8) = 6.6.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.