Pembahasan Soal Ujian Profesi Aktuaris
Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
Mata Ujian | : | Metoda Statistika |
Periode Ujian | : | November 2018 |
Nomor Soal | : | 18 |
SOAL
Misalkan ada 100 pengamatan dan diketahui
\(Var\left[ {\hat S\left( t \right)} \right] = 0,00056;{\rm{ }}Var\left[ {\hat S\left( r \right)} \right] = 0,00040\)
Jika \(S\left( t \right) > 2S\left( r \right)\) dan , Tentukanlah \(100Cov\left[ {\hat S\left( t \right),\hat S\left( r \right)} \right]\)
- 0,0010
- 0,0015
- 0,0020
- 0,0025
- 0,0030
Diketahui | \(Var\left[ {\hat S\left( t \right)} \right] = 0,00056;{\rm{ }}Var\left[ {\hat S\left( r \right)} \right] = 0,00040\)
\(S\left( t \right) > 2S\left( r \right)\) dengan \(t < r\) |
Rumus yang digunakan | \(Var\left[ {\hat S\left( t \right)} \right] = Var\left[ {\frac{{{N_t}}}{n}} \right] = \frac{{S\left( t \right)F\left( t \right)}}{n}\)
\(Cov\left[ {\hat S\left( t \right),\hat S\left( r \right)} \right] = \frac{{S\left( t \right)S\left( r \right)}}{n}\) |
Proses Pengerjaan |
\(100Cov\left[ {\hat S\left( t \right),\hat S\left( r \right)} \right] = \frac{{100 \cdot {q_t} \cdot {q_r}}}{n}\)
\(= \frac{{100 \cdot 0,059545 \cdot 0,0417424}}{{100}}\)
\(= 0,00224\) |
Jawaban | d. 0,0025 |