Pembahasan Ujian PAI: A60 - No. 7 - November 2018

Pembahasan Soal Ujian Profesi Aktuaris

Institusi	:	Persatuan Aktuaris Indonesia (PAI)
Mata Ujian	:	Matematika Aktuaria
Periode Ujian	:	November 2018
Nomor Soal	:	7

SOAL

Perhatikan select survival distribution berikut:

\({S_T}(t;x) = \left( {1 – \frac{t}{{40 – x}}} \right),0 \le x < 40\) dan \(0 < t < 40 – x.\)

Jika \({}_4{p_{_{[30]}}} = a\) dan \(\mathop e\limits^O \)\(_{_{[30]}} = b\)
Berapakah nilai ab (a dikali b)?

Diketahui	\(T \sim Uniform\)
Step 1	\({}_4{p_{_{[30]}}} = a\) \({}_4{p_{_{[30]}}} = \left( {1 – \frac{4}{{40 – 30}}} \right)\) \({}_4{p_{_{[30]}}} = 0,6\) \(a = 0,6\)
Step 2	\(\mathop e\limits^O \)\(_{{}_{_{[30]}}} = b\) \(\mathop e\limits^O \)\(_{_{[30]}} = \int\limits_0^{40 – 30} {{S_T}(t;x)dt} \) \(\mathop e\limits^O \)\(_{_{[30]}} = \int\limits_0^{40 – 30} {1 – \frac{t}{{40 – 30}}dt} \) \(\mathop e\limits^O \)\(_{_{[30]}} = \int\limits_0^{10} {1 – \frac{t}{{10}}dt} \) \(\mathop e\limits^O \)\(_{_{[30]}} = 10 – \frac{{{{10}^2}}}{{(2)10}}\) \(\mathop e\limits^O \)\(_{_{[30]}} = 5\) \(b = 5\)
Maka	\(ab = 0,6(5)\) \(ab = 3\)
Jawaban	b. 3

Pembahasan Ujian PAI: A60 – No. 7 – November 2018