Pembahasan Ujian PAI: A50 - No. 6 - Juni 2015

Institusi	:	Persatuan Aktuaris Indonesia (PAI)
Mata Ujian	:	Metoda Statistika
Periode Ujian	:	Juni 2015
Nomor Soal	:	6

SOAL

Diketahui fungsi force of mortality \(\begin{array}{*{20}{c}} {\mu \left( x \right) = \frac{1}{{x + 1}},}&{x \ge 0} \end{array}\)

Tentukan \(S\left( x \right)\)

\(\begin{array}{*{20}{c}} {S\left( x \right) = \frac{1}{{x + 1}},}&{x \ge 0} \end{array}\)
\(\begin{array}{*{20}{c}} {S\left( x \right) = \frac{x}{{x + 1}},}&{x \ge 0} \end{array}\)
\(\begin{array}{*{20}{c}} {S\left( x \right) = {e^{x + 1}},}&{x \ge 0} \end{array}\)
\(\begin{array}{*{20}{c}} {S\left( x \right) = \frac{{x + 1}}{x},}&{x \ge 0} \end{array}\)
\(\begin{array}{*{20}{c}} {S\left( x \right) = \frac{1}{{{{\left( {x + 1} \right)}^2}}},}&{x \ge 0} \end{array}\)

Diketahui	\(\begin{array}{*{20}{c}} {\mu \left( x \right) = \frac{1}{{x + 1}},}&{x \ge 0} \end{array}\)
Rumus yang digunakan	\(S\left( x \right) = \exp \left[ { – \int\limits_0^x {\mu \left( t \right)dt} } \right]\)
Proses pengerjaan	\(S\left( x \right) = \exp \left[ { – \int\limits_0^x {\left( {\frac{1}{{t + 1}}} \right)dt} } \right] = \exp \left[ { – \ln \left( {x + 1} \right)} \right] = \frac{1}{{x + 1}}\)
Jawaban	*a. \(\begin{array}{{20}{c}} {S\left( x \right) = \frac{1}{{x + 1}},}&{x \ge 0} \end{array}\)**