Pembahasan Ujian PAI: A50 – No. 7 – Juni 2016

By Fery Widhiatmoko On Mar 28, 2019

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 \(e_{20}^ \circ \)

Fery Widhiatmoko 564 posts 11 comments

Merupakan lulusan Magister Matematika minat Aktuaria dari Universitas Gadjah Mada.

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