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(Created page with "'''Answer: D''' <math>\hat{S}(21.0)=\frac{59}{60} \times \frac{59-8+1-1}{59-8+1} \times \frac{51-6+7-2}{51-6+7} \times \frac{50-7+7-1}{50-7+7} \times \frac{49-6+5-1}{49-6+5}=0.8899</math> <math>\operatorname{Var}[\hat{S}(21.0)] \approx 0.8899^{2}\left(\frac{1}{60 \times 59}+\frac{1}{52 \times 51}+\frac{2}{52 \times 50}+\frac{1}{50 \times 49}+\frac{1}{48 \times 47}\right)=0.00181</math> The upper limit of the <math>80 \%</math> linear confidence interval is <math disp...") |
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0.8899+1.282(0.00181)^{0.5}=0.944 | 0.8899+1.282(0.00181)^{0.5}=0.944 | ||
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Revision as of 02:33, 18 January 2024
Answer: D
[math]\hat{S}(21.0)=\frac{59}{60} \times \frac{59-8+1-1}{59-8+1} \times \frac{51-6+7-2}{51-6+7} \times \frac{50-7+7-1}{50-7+7} \times \frac{49-6+5-1}{49-6+5}=0.8899[/math]
[math]\operatorname{Var}[\hat{S}(21.0)] \approx 0.8899^{2}\left(\frac{1}{60 \times 59}+\frac{1}{52 \times 51}+\frac{2}{52 \times 50}+\frac{1}{50 \times 49}+\frac{1}{48 \times 47}\right)=0.00181[/math]
The upper limit of the [math]80 \%[/math] linear confidence interval is
[[math]]
0.8899+1.282(0.00181)^{0.5}=0.944
[[/math]]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.