Pembahasan Soal Ujian Profesi Aktuaris
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 |
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| 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. \(n{\delta ^2}\) |