Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Statistika |
| Periode Ujian | : | Mei 2018 |
| Nomor Soal | : | 5 |
SOAL
Diberikan
\({\rm{i}}{\rm{. }}\mu _x^{} = \left\{ \begin{array}{l} 0.03,30 \le x < 40\\ 0.04 + 0.001{(x – 40)^2},40 \le x < 50 \end{array} \right.\)
Hitunglah nilai \(_{4|11}{q_{30}}\)
- 0.305
- 0.325
- 0.355
- 0.375
- 0.4
| Diketahui | \({\rm{i}}{\rm{. }}\mu _x^{} = \left\{ \begin{array}{l} 0.03,30 \le x < 40\\ 0.04 + 0.001{(x – 40)^2},40 \le x < 50 \end{array} \right.\) |
| Rumus yang digunakan | \(_{t|u}{q_x}{ = _t}{p_x}{._u}{q_{x + t}}\) |
| Proses pengerjaan | Dengan mengaplikasi rumus diatas diperoleh
Berdasarkan
\(_4{p_{30}} = {e^{ – \int\limits_{30}^{34} {{\rm{0}}{\rm{.03 }}dx} }} = 0.88692\)
\(_{11}{p_{34}} = {e^{ – (\int\limits_{34}^{40} {{\rm{0}}{\rm{.03 }}dx} + \int\limits_{40}^{45} {0.04 + 0.001{{(x – 40)}^2}{\rm{ }}dx)} }} = 0.655953\)
\(_{4|11}{q_{30}}{ = _4}{p_{30}}{._{11}}{q_{34}}\)
\({\rm{ }}{ = _4}{p_{30}}.(1{ – _{11}}{p_{34}})\)
\({\rm{ = }}(0.88692)*(1 – 0.655953)\)
\({\rm{ }} = {\rm{ 0}}{\rm{.305}}\) |
| Jawaban | a. 305 |
