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)?
- 1
- 3
- 5
- 7
- 9
| 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 |
