Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Diketahui survival function \(s\left( x \right)\) sebagai berikut:
\({s\left( x \right) = 1,}\) \({0 \le x < 1}\) \({s\left( x \right) = 1 – \frac{{{e^x}}}{{100}},}\) \({1 \le x < 4.5}\) \({s\left( x \right) = 0,}\) \({4.5 \le x}\)Hitunglah \(\mu \left( 4 \right)\)
- 1,202552
- 0,908307
- 0,545982
- 0,454018
- 0,251338
| Diketahui | survival function \(s\left( x \right)\) sebagai berikut: \({s\left( x \right) = 1,}\) \({0 \le x < 1}\) \({s\left( x \right) = 1 – \frac{{{e^x}}}{{100}},}\) \({1 \le x < 4.5}\) \({s\left( x \right) = 0,}\) \({4.5 \le x}\) |
| Rumus yang digunakan | \(\mu \left( x \right) = – \frac{1}{{S\left( x \right)}} \cdot \frac{d}{{dx}}S\left( x \right)\) |
| Proses pengerjaan | \(\mu \left( 4 \right) = – \frac{1}{{S\left( 4 \right)}} \cdot \frac{d}{{dx}}S\left( 4 \right) = – \frac{1}{{1 – \frac{{{e^4}}}{{100}}}} \cdot \frac{d}{{dx}}\left( {1 – \frac{{{e^4}}}{{100}}} \right)\) \(\mu \left( 4 \right) = \frac{{100}}{{100 – {e^4}}} \cdot \frac{{{e^4}}}{{100}}\) \(\mu \left( 4 \right) = 1.202553\) |
| Jawaban | a. 1,202552 |