Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Statistika |
| Periode Ujian | : | Mei 2017 |
| Nomor Soal | : | 26 |
SOAL
Korelasi serial order pertama (first order serial correlation) yaitu \({\varepsilon _t} = \rho {\varepsilon _{t – 1}} + {v_t}\). Nilai \(\rho = 0.6,{\rm{ }}Var\left[ v \right] = 40\). Hitunglah \(Var\left[ \varepsilon \right]\)
- 44.5
- 49
- 53.5
- 58.0
- 62.5
| Diketahui | \(\rho = 0.6\)
\({\rm{Var}}\left[ v \right] = {\sigma _v}^2 = 40\) |
| Rumus yang digunakan | \(Var\left[ \varepsilon \right] = \frac{{{\sigma _v}^2}}{{1 – {\rho ^2}}}\) |
| Proses pengerjaan | \(Var\left[ \varepsilon \right] = \frac{{{\sigma _v}^2}}{{1 – {\rho ^2}}}\)
\(= \frac{{40}}{{1 – {{0.6}^2}}}\)
\(= 62.5\) |
| Jawaban | e. 62.5 |
