Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Matematika Aktuaria |
| Periode Ujian | : | November 2018 |
| Nomor Soal | : | 26 |
SOAL
Diketahui:
- \({\mu _{x + t}} = c,t \ge 0\)
- \(\delta = 0,08\)
- \({\bar A_x} = 0,3343\)
- \({T_x}\) adalah random variable untuk future lifetime (x)
Tentukanlah \(Var[{\bar a_{\left. {\overline {\, {{T_x}} \,}}\! \right| }}]!\)
- 12
- 14
- 16
- 18
- 20
| 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 |
