Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | A60 – Matematika Aktuaria |
| Periode Ujian | : | November 2017 |
| Nomor Soal | : | 29 |
SOAL
Manakah dari pernyataan berikut yang benar untuk \(\frac{\partial }{{\partial n}}{}_n|{\bar a_x}\)
- \(\frac{\partial }{{\partial n}}\int\limits_n^\infty {{v^t}\,\,{}_t{q_x}\,\,dt} \)
- \(\frac{\partial }{{\partial n}}\int\limits_n^\infty {{v^t}\,\,{}_t{p_{x + n}}\,\,dt} \)
- \({v^n}\,\,{}_n{p_x}\)
- \(– {}_n{E_x}\)
- \({v^n}\,\,{}_n{E_x}\)
| Rumus | \({}_n|{\bar a_x} = \int\limits_n^\infty {{v^t}\,\,{}_t{p_x}\,\,dt} \)
\({}_n{E_x} = \,{v^n}{}_n{p_x}\) |
| Step 1 | \(\frac{\partial }{{\partial n}}{}_n|{\bar a_x} = \frac{\partial }{{\partial n}}\int\limits_n^\infty {{v^t}\,\,{}_t{p_x}\,\,dt} \)
\(\frac{\partial }{{\partial n}}{}_n|{\bar a_x} = {v^\infty }{}_\infty {p_x}\,\, – \,\,{v^n}{}_n{p_x}\)
\(\frac{\partial }{{\partial n}}{}_n|{\bar a_x} = 0 – \,\,{v^n}{}_n{p_x}\)
\(\frac{\partial }{{\partial n}}{}_n|{\bar a_x} = – \,\,{v^n}{}_n{p_x}\)
\(\frac{\partial }{{\partial n}}{}_n|{\bar a_x} = – {}_n{E_x}\) |
| Jawaban | d. \(– {}_n{E_x}\) |
