Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Berdasarkan soal nomor 2
Tentukan Probability Density Function dari \(X\).
- \({e^{ – x}}\left( {x + 2} \right)\)
- \({e^{ – x}}{x^2}\)
- \({e^{ – x}}{\left( {x + 1} \right)^2}\)
- \(\left( {{e^{ – x}} + 1} \right)x\)
- \({e^{ – x}}x\)
| Diketahui | \(\begin{array}{*{20}{c}} {S\left( x \right) = {e^{ – x}}\left( {x + 1} \right),}&{x \ge 0} \end{array}\) |
| Rumus yang digunakan | \(f\left( x \right) = – \frac{d}{{dx}}S\left( x \right)\) |
| Proses pengerjaan | \(f\left( x \right) = – \frac{d}{{dx}}\left[ {{e^{ – x}}\left( {x + 1} \right)} \right]\) \(f\left( x \right) = – \frac{d}{{dx}}\left( {x \cdot {e^{ – x}}} \right) – \frac{d}{{dx}}\left( {{e^{ – x}}} \right)\) \(f\left( x \right) = \left( { – {e^{ – x}} + x{e^{ – x}}} \right) + {e^{ – x}}\) \(f\left( x \right) = x{e^{ – x}}\) |
| Jawaban | e. \({e^{ – x}}x\) |