Pembahasan Soal Ujian Profesi Aktuaris
Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
Mata Ujian | : | Matematika Aktuaria |
Periode Ujian | : | Juni 2015 |
Nomor Soal | : | 20 |
SOAL
Diberikan suatu kematian mengikuti \({l_x} = 100 – x\); \(0 \le x \le 100\)
Hitunglah \({e_{85,2}}\) (gunakan pembulatan terdekat)
- 6.890
- 6.895
- 6.900
- 6.905
- 6.910
Diketahui | \({l_x} = 100 – x\); \(0 \le x \le 100\) |
Rumus yang digunakan | \({}_t{p_x} = \frac{{{l_{x + t}}}}{{{l_x}}}\)
\({e_x} = \sum\limits_{k = 1}^\infty {{}_k{p_x}} \)
\(\sum\limits_{k = 1}^n k = \frac{{n\left( {n + 1} \right)}}{2}\) |
Proses Pengerjaan | \({e_{85.2}} = \sum\limits_{k = 1}^{14} {{}_k{p_{85.2}}} = \sum\limits_{k = 1}^\infty {\frac{{{l_{85.2 + k}}}}{{{l_{85.2}}}}} \)
\({e_{85.2}} = \sum\limits_{k = 1}^{14} {\frac{{100 – 85.2 – k}}{{100 – 85.2}}} \)
\({e_{85.2}} = \sum\limits_{k = 1}^{14} {\frac{{14.8}}{{14.8}}} – \sum\limits_{k = 1}^{14} {\frac{k}{{14.8}}} \)
\({e_{85.2}} = 14 – \frac{{\frac{{\left( {14} \right)\left( {15} \right)}}{2}}}{{14.8}}\)
\({e_{85.2}} = 6.90541\) |
Jawaban | d. 6.905 |