Pembahasan Soal Ujian Profesi Aktuaris
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)?
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| 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 |