Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Aktuaria |
| Periode Ujian |
: |
November 2017 |
| Nomor Soal |
: |
20 |
SOAL
Diberikan bahwa kematian mengikuti \({l_x} = 100 – x,\,\,\,0 \le x \le 100\)
Hitunglah \({e_{80}}\)
- 6,75
- 8,75
- 9,25
- 10,45
- 11,35
| Rumus |
\({e_{80}} = \sum\limits_{k = 1}^\infty {{}_k{P_{80}}} \) |
| Kalkulasi |
\({e_{80}} = \sum\limits_{k = 1}^\infty {\frac{{{l_{80 + k}}}}{{{l_{80}}}}} \)
\({e_{80}} = \frac{1}{{{l_{80}}}}\sum\limits_{k = 1}^\infty {{l_{80 + k}}} \)
\({e_{80}} = \frac{1}{{100 – 80}}\sum\limits_{k = 1}^\infty {\left( {100 – 80 – k} \right)} \)
\({e_{80}} = \frac{1}{{20}}\sum\limits_{k = 1}^\infty {\left( {20 – k} \right)} \)
\({e_{80}} = \frac{1}{{20}}\left( {19 + 18 + 17 + … + 1 + 0} \right)\)
\({e_{80}} = \frac{1}{{20}}\left( {\frac{{20(19 + 0)}}{2}} \right)\)
\({e_{80}} = 9,5\) |
| Jawaban |
Tidak tersedia pada pilihan |
