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<math>\Rightarrow s d[\hat{S}(25)] \approx 0.8940 \sqrt{\left(\frac{1}{29 \times 28}+\frac{2}{27 \times 25}\right)}=0.0579</math> | <math>\Rightarrow s d[\hat{S}(25)] \approx 0.8940 \sqrt{\left(\frac{1}{29 \times 28}+\frac{2}{27 \times 25}\right)}=0.0579</math> | ||
{{soacopyright|2024}} | {{soacopyright|2024}} | ||
Latest revision as of 02:39, 18 January 2024
Answer: C
[math]s d[\hat{S}(25)] \approx \hat{S}(25) \sqrt{\sum_{t_{(j)} \leq 25} \frac{d_{j}}{r_{j}\left(r_{j}-d_{j}\right)}}[/math]
[math]\hat{S}(25)=\hat{p}_{1} \times \hat{p}_{2}=0.8940[/math]
[math]d_{1}=r_{1}\left(1-\hat{p}_{1}\right)=1 ; \quad d_{2}=r_{2}\left(1-\hat{p}_{2}\right)=2[/math]
[math]\Rightarrow s d[\hat{S}(25)] \approx 0.8940 \sqrt{\left(\frac{1}{29 \times 28}+\frac{2}{27 \times 25}\right)}=0.0579[/math]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.