Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Matematika Aktuaria |
| Periode Ujian | : | November 2015 |
| Nomor Soal | : | 12 |
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. \({}_{\frac{1}{4}}{p_x}\) |
