Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Sebuah distribusi Gamma memiliki rata-rata/ (“mean”) = 8 dan skewness = 1. Hitung Variansinya?
- 12
- 16
- 61
- 8
| Diketahui |
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| Rumus yang digunakan |
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| Proses pengerjaan | \(\mu = \bar X = {{\mu ‘}_1} = \alpha \theta \) \({{\mu ‘}_2} = {\alpha ^2}{\theta ^2} – \alpha {\theta ^2}\) \({{\mu ‘}_3} = {\rm{ }}({\alpha ^3} – 3{\alpha ^2} + 2\alpha ){\theta ^3}\) \(\mu 3 = {{\mu ‘}_3} – 3{{\mu ‘}_2}\mu + 2{\mu ^3} = 2\alpha {\theta ^3}\) \(skewness = {\mu ^3}{\sigma ^3} = \frac{{2\alpha {\theta ^3}}}{{{{({\sigma ^3}^{/2})}^2}}} = 1 \to \alpha = 4\) Diketahui pula bahwa \(\mu = \alpha \theta = 8\) , dengan demikian kita dapatkan \(\theta = 2\) \(Varians = {\sigma ^2} = \alpha {\theta ^2} = 4{(2)^2} = 16\) |
| Jawaban | b. 16 |