779 Share Pembahasan Soal Ujian Profesi Aktuaris Institusi : Persatuan Aktuaris Indonesia (PAI) Mata Ujian : Matematika Aktuaria Periode Ujian : November 2018 Nomor Soal : 9 SOAL Perhatikan fungsi survival berikut: \({S_0}(x) = {\left( {1 – \frac{x}{{60}}} \right)^{\frac{1}{3}}},0 \le x \le 60\) Berapakah \({\mu _{35}}?\) 0,0201 0,0167 0,0133 0,0067 0,0023 Kunci Jawaban & Pembahasan Maka \({\mu _x} = \frac{{ – \frac{d}{{dt}}S(x)}}{{S(x)}}\) \({\mu _x} = \frac{{ – \frac{d}{{dt}}{{\left( {1 – \frac{x}{{60}}} \right)}^{\frac{1}{3}}}}}{{{{\left( {1 – \frac{x}{{60}}} \right)}^{\frac{1}{3}}}}}\) \({\mu _x} = \frac{{ – \frac{1}{3}\left( { – \frac{1}{{60}}} \right){{\left( {1 – \frac{x}{{60}}} \right)}^{ – \frac{2}{3}}}}}{{{{\left( {1 – \frac{x}{{60}}} \right)}^{\frac{1}{3}}}}}\) \({\mu _{35}} = \frac{{ – \frac{1}{3}\left( { – \frac{1}{{60}}} \right){{\left( {1 – \frac{{35}}{{60}}} \right)}^{ – \frac{2}{3}}}}}{{{{\left( {1 – \frac{{35}}{{60}}} \right)}^{\frac{1}{3}}}}}\) \({\mu _{35}} = \frac{1}{{75}}\) \({\mu _{35}} \cong 0,0133\) Jawaban c. 0,0133 A60AktuariaEdukasiMatematika AktuariaPAIUjian Profesi 779 Share