Pembahasan Soal Ujian Profesi Aktuaris
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 |
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| Jawaban | d. 0,0025 |