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Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Pemodelan dan Teori Risiko |
| Periode Ujian | : | November 2018 |
| Nomor Soal | : | 14 |
SOAL
Diketahui :
Tentukan nilai \(q\)
| Diketahui |
|
| Rumus yang digunakan | Binomial: \({E\left[ N \right] = mq,}\) \({Var\left[ N \right] = mq\left( {1 – q} \right)}\) |
| Proses pengerjaan | \(E\left[ N \right] = \mu = mq = 34,574\) dan \(Var\left[ N \right] = {\sigma ^2} = mq\left( {1 – q} \right)\)
\({\lambda _F} = {\left( {\frac{{{z_p}}}{r}} \right)^2}\left[ {\frac{{{\sigma ^2}}}{\mu }} \right]\) |
| \({\lambda _F} = {\left( {\frac{{{z_{0.95}}}}{r}} \right)^2}\left[ {\frac{{{\sigma ^2}}}{\mu }} \right]\) \(34,574 = {\left( {\frac{{1.96}}{{0.01}}} \right)^2}\left( {\frac{{mq\left( {1 – q} \right)}}{{mq}}} \right)\) \(34,574 = 38,416\left( {1 – q} \right)\) \(q = 1 – \frac{{34,574}}{{38,416}} = 0.1\) |
|
| Jawaban | b. 0,10 |
Merupakan lulusan Magister Matematika minat Aktuaria dari Universitas Gadjah Mada.
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