Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Kematian berdistribusi berdistribusi seragam diantara “integrated ages”. Manakah diantara pernyataan berikut yang merepresentasikan \({}_{\frac{3}{4}}{p_x} + \frac{1}{2} \cdot {}_{\frac{1}{2}}{p_x}{\mu _{x + \frac{1}{2}}}\)?
- \({}_{\frac{3}{4}}{p_x}\)
- \({}_{\frac{3}{4}}{q_x}\)
- \({}_{\frac{1}{2}}{p_x}\)
- \({}_{\frac{1}{2}}{q_x}\)
- \({}_{\frac{1}{4}}{p_x}\)
| Diketahui | Kematian berdistribusi berdistribusi seragam diantara “integrated ages” |
| Rumus yang digunakan | \({}_s{p_x} = 1 – s \cdot {q_x}\) \({}_s{p_x}{\mu _{x + s}} = {q_x}\) |
| Proses pengerjaan | \({}_{\frac{3}{4}}{p_x} + \frac{1}{2} \cdot {}_{\frac{1}{2}}{p_x}{\mu _{x + \frac{1}{2}}}\) \(= 1 – \frac{3}{4}{q_x} + \frac{1}{2}\left( {{q_x}} \right)\) \(= 1 – \frac{1}{4}{q_x}\) \(= {}_{\frac{1}{4}}{p_x}\) |
| Jawaban | e. \({}_{\frac{1}{4}}{p_x}\) |