Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Matematika Aktuaria |
| Periode Ujian |
: |
November 2015 |
| Nomor Soal |
: |
24 |
SOAL
Hitunglah nilai dari \(Var\left[ {{S_n}} \right]\) pada soal nomor 23
- \(\delta \)
- \({\delta ^2}\)
- \(n\delta \)
- \(n{\delta ^2}\)
- \(\frac{{{\delta ^2}}}{n}\)
| Diketahui |
- Misalkan \({X_1},{X_2}, \ldots ,{X_n}\) suatu variabel acak yang bebas, sehingga setiap \({X_i}\) memiliki “expected value ”\(\mu \) dan variansi .
- \({S_n} = {X_1} + {X_2} + \cdots + {X_n}\)
|
| Rumus yang digunakan |
\(Var\left[ {{X_1} + {X_2} + \cdots + {X_n}} \right] = Var\left[ {{X_1}} \right] + Var\left[ {{X_2}} \right] + \cdots Var\left[ {{X_n}} \right]\) |
| Proses pengerjaan |
\(Var\left[ {{S_n}} \right] = Var\left[ {{X_1} + {X_2} + \cdots + {X_n}} \right]\)
\(Var\left[ {{S_n}} \right] = Var\left[ {{X_1}} \right] + Var\left[ {{X_2}} \right] + \cdots + Var\left[ {{X_n}} \right]\)
\(Var\left[ {{S_n}} \right] = {\delta _1}^2 + {\delta _2}^2 + \cdots + {\delta _n}^2\)
\(Var\left[ {{S_n}} \right] = n{\delta ^2}\) |
| Jawaban |
d. \(n{\delta ^2}\) |
