Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Jika \(X\) berdistribusi seragam pada \(\left( {1,3} \right)\), berapakah \(Var\left( X \right)\)?
- 1
- \(\frac{1}{3}\)
- \(\frac{2}{3}\)
- 2
- 3
| Diketahui | \(X\) berdistribusi seragam pada \(\left( {1,3} \right)\) |
| Rumus yang digunakan | Uniform: \(E\left[ X \right] = \frac{{b + a}}{2}\) dan \(Var\left[ X \right] = \frac{{{{\left( {b – a} \right)}^2}}}{{12}}\) |
| Proses pengerjaan | \(Var\left[ X \right] = \frac{{{{\left( {b – a} \right)}^2}}}{{12}} = \frac{{{{\left( {3 – 1} \right)}^2}}}{{12}} = \frac{1}{3}\) |
| Jawaban | b. \(\frac{1}{3}\) |