Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Dengan menggunakan data nomor 17, estimasikan \(q_{20}^{‘\left( d \right)}\) dengan menggunakan distribusi exponential untuk kejadian meninggal dan penarikan tersebut
- 0,0216831
- 0,0101017
- 0,0101536
- 0,0101145
- 0,0100721
| Diketahui |
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| Rumus yang digunakan | \({\hat q_x} = \frac{{{d_x}}}{{{n_x} – \left( {1 – s} \right) \cdot {c_x} + \left( {1 – r} \right) \cdot {k_x}}}\) Asumsi distribusi exponential \(\begin{array}{*{20}{c}} {q_x^{‘\left( d \right)} = 1 – {{\left( {p_x^{\left( \tau \right)}} \right)}^{\frac{{q_x^{\left( d \right)}}}{{q_x^{\left( d \right)} + q_x^{\left( w \right)}}}}},}&{p_x^{\left( \tau \right)} = 1 – q_x^{\left( d \right)} – q_x^{\left( w \right)}} \end{array}\) |
| Proses pengerjaan | \(p_x^{\left( \tau \right)} = 1 – q_x^{\left( d \right)} – q_x^{\left( w \right)} = 1 – 0.01 – 0.03 = 0.96\) |
| \(q_x^{‘\left( d \right)} = 1 – {\left( {p_x^{\left( \tau \right)}} \right)^{\frac{{q_x^{\left( d \right)}}}{{q_x^{\left( d \right)} + q_x^{\left( w \right)}}}}} = 1 – {\left( {0.96} \right)^{\frac{{0.01}}{{0.01 + 0.03}}}} = 0.010153599\) | |
| Jawaban | c. 0,0101536 |