423 Share Pembahasan Soal Ujian Profesi Aktuaris Institusi : Persatuan Aktuaris Indonesia (PAI) Mata Ujian : Metoda Statistika Periode Ujian : Juni 2016 Nomor Soal : 7 SOAL Jika diketahui \(e_0^ \circ = 40\) \(S\left( x \right) = 1 – \frac{x}{\omega }{\rm{,}}\) atau \(0 \le x \le \omega \) Hitunglah \(e_{20}^ \circ \) 30 36 40 42 50 Kunci Jawaban & Pembahasan Diketahui \(e_0^ \circ = 40\) \(S\left( x \right) = 1 – \frac{x}{\omega }{\rm{,}}\) untuk \(0 \le x \le \omega \) Rumus yang digunakan \({}_t{p_x} = \frac{{S\left( {x + t} \right)}}{{S\left( x \right)}}\) \(e_x^ \circ = \int\limits_0^\infty {{}_t{p_x}dt} \) Proses Pengerjaan \({}_t{p_x} = \frac{{S\left( {x + t} \right)}}{{S\left( x \right)}} = \frac{{\frac{{\omega – x – t}}{\omega }}}{{\frac{{\omega – x}}{\omega }}}\) \(= \frac{{\omega – x – t}}{{\omega – x}}\) \(e_0^ \circ = \int\limits_0^\omega {\frac{{\omega – t}}{\omega }dt} \) \(= \left. {\frac{{\omega t – \frac{1}{2}{t^2}}}{\omega }} \right|_0^\omega \)z \(= \omega – \frac{1}{2}\omega \) \(40 = \frac{1}{2}\omega \) \(\omega = 80\) \(e_{20}^ \circ = \int\limits_0^{60} {{}_t{p_{20}}dt} \) \(= \int\limits_0^{60} {\frac{{60 – t}}{{60}}dt} \) \(= \left. {\frac{{60t – \frac{1}{2}{t^2}}}{{60}}} \right|_0^{60}\) \(= 60 – 30\) \(= 30\) Jawaban a. 30 A50AktuariaEdukasiMetoda StatistikaPAIUjian Profesi Aktuaris 423 Share