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. \({}_{\frac{1}{4}}{p_x}\) |
