26 April, 2024

Pembahasan Ujian PAI: A60 – No. 26 – November 2018

11 January 2019

by Abinaila Taim

with no comment

A60 - Matematika Aktuaria Aktuaria Edukasi Pembahasan Ujian Profesi Aktuaris (Persatuan Aktuaris Indonesia / PAI)

Pembahasan Soal Ujian Profesi Aktuaris

Institusi	:	Persatuan Aktuaris Indonesia (PAI)
Mata Ujian	:	Matematika Aktuaria
Periode Ujian	:	November 2018
Nomor Soal	:	26

SOAL

Diketahui:

Tentukanlah \(Var[{\bar a_{\left. {\overline {\, {{T_x}} \,}}\! \right| }}]!\)

by Auditya Brilliant Asuransi Umum

by Abinaila Taim A10 - Matematika Keuangan

by Abinaila Taim A10 - Matematika Keuangan

by Ir. Sudarno Hardjo Saparto AAIK, ICPU, ICBU, QIP, CIIB, AMRP, AK3 Asuransi Umum

by Nasrun A Yusuf Asuransi Jiwa

by Ir. Sudarno Hardjo Saparto AAIK, ICPU, ICBU, QIP, CIIB, AMRP, AK3 Asuransi Kebakaran

©

2024

Step 1	\({\bar A_x} = \frac{\mu }{{\mu + \delta }}\) \(0,3443 = \frac{\mu }{{\mu + 0,08}}\) \(\mu = \,0,0420070154\)
Step 2	\({}^2{\bar A_x} = \,\frac{\mu }{{\mu + 2\delta }}\) \({}^2{\bar A_x} = 0,2079482998\)
Step 3	\(Var[{\bar Z_x}] = {}^2{\bar A_x} – {\bar A_x}{}^2\) \(Var[{\bar Z_x}] = 0,2079482998 – 0,3443{}^2\) \(Var[{\bar Z_x}] = 0,08940580981\)
Step 4	\(Var[{\bar a_{\left. {\overline {\, {{T_x}} \,}}\! \right\| }}] = \frac{{Var[{{\bar Z}_x}]}}{{{{(\delta )}^2}}}\) \(Var[{\bar a_{\left. {\overline {\, {{T_x}} \,}}\! \right\| }}] = \frac{{0,08940580981}}{{{{\left[ {0,08} \right]}^2}}}\) \(Var[{\bar a_{\left. {\overline {\, {{T_x}} \,}}\! \right\| }}] = 13,96965778\) \(Var[{\bar a_{\left. {\overline {\, {{T_x}} \,}}\! \right\| }}]\, \simeq \,14\)
Jawaban	b. 14