Pembahasan Ujian PAI: A50 – No. 8 – November 2015

By Fery Widhiatmoko On Apr 16, 2019

Pembahasan Soal Ujian Profesi Aktuaris

Institusi	:	Persatuan Aktuaris Indonesia (PAI)
Mata Ujian	:	Metoda Statistika
Periode Ujian	:	November 2015
Nomor Soal	:	8

SOAL

Jika diketahui \(q_x^{‘\left( d \right)} = 0,2\) dan \(q_x^{‘\left( w \right)} = 0,4\). Hitunglah \(q_x^{\left( \tau \right)}\)

Fery Widhiatmoko 564 posts 11 comments

Merupakan lulusan Magister Matematika minat Aktuaria dari Universitas Gadjah Mada.

Diketahui	\(q_x^{‘\left( d \right)} = 0,2\) dan \(q_x^{‘\left( w \right)} = 0,4\)
Rumus yang digunakan	\(q_x^{\left( d \right)} = q_x^{‘\left( d \right)}\left( {1 – \frac{1}{2}q_x^{‘\left( w \right)}} \right){\rm{ }}\) dan \(q_x^{\left( w \right)} = q_x^{‘\left( w \right)}\left( {1 – \frac{1}{2}q_x^{‘\left( d \right)}} \right)\) \(q_x^{\left( \tau \right)} = q_x^{\left( d \right)} + q_x^{\left( w \right)}\)
Proses pengerjaan	\(q_x^{\left( d \right)} = q_x^{‘\left( d \right)}\left( {1 – \frac{1}{2}q_x^{‘\left( w \right)}} \right)\) \(= 0,2\left( {1 – \frac{{0,4}}{2}} \right)\) \(= 0,16\)
	\(q_x^{\left( w \right)} = q_x^{‘\left( w \right)}\left( {1 – \frac{1}{2}q_x^{‘\left( d \right)}} \right)\) \(= 0,4\left( {1 – \frac{{0,2}}{2}} \right)\) \(= 0,36\)
	\(q_x^{\left( \tau \right)} = q_x^{\left( d \right)} + q_x^{\left( w \right)}\) \(= 0,16 + 0,36\) \(= 0,52\)
Jawaban	e. 0,52