Pembahasan Soal Ujian Profesi Aktuaris
Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
Mata Ujian |
: |
Metoda Statistika |
Periode Ujian |
: |
Juni 2015 |
Nomor Soal |
: |
13 |
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 |