Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Diberikan model regresi dibawah ini
\({Y_i} = {\beta _1} + {\beta _2}{X_{2i}} + {\beta _3}{X_{3i}} + {\varepsilon _i}\)
diketahui
\(\sum\limits_{}^{} {X_{2i}^2 = 1200} \) \(\sum\limits_{}^{} {X_{3i}^2 = 2200} \) \(\sum\limits_{}^{} {X_{2i}^{}X_{3i}^{} = 2500} \) \({s^2} = 1000\)Hitunglah \(\widehat {Cov}(\widehat {{\beta _2}},\widehat {{\beta _3}})\)
- 0.5612
- 0.6925
- 0.7125
- 0.7513
- 0.8276
| Diketahui | \(\sum\limits_{}^{} {X_{2i}^2 = 1200} \) \(\sum\limits_{}^{} {X_{3i}^2 = 2200} \) \(\sum\limits_{}^{} {X_{2i}^{}X_{3i}^{} = 2500} \) \({s^2} = 1000\) |
| Rumus yang digunakan | \(\widehat {Cov}(\widehat {{\beta _2}},\widehat {{\beta _3}}) = \frac{{ – {s^2}\frac{{\sum {{X_{2i}}{X_{3i}}} }}{{\sqrt {\sum {X_{2i}^2\sum {X_{3i}^2} } } }}}}{{(1 – {{(\frac{{\sum {{X_{2i}}{X_{3i}}} }}{{\sqrt {\sum {X_{2i}^2\sum {X_{3i}^2} } } }})}^2})(\sqrt {\sum {X_{2i}^2\sum {X_{3i}^2} } } )}}\) |
| Proses pengerjaan | \(\widehat {Cov}(\widehat {{\beta _2}},\widehat {{\beta _3}}) = \frac{{ – {s^2}\frac{{\sum {{X_{2i}}{X_{3i}}} }}{{\sqrt {\sum {X_{2i}^2\sum {X_{3i}^2} } } }}}}{{(1 – \frac{{\sum {{X_{2i}}{X_{3i}}} }}{{\sqrt {\sum {X_{2i}^2\sum {X_{3i}^2} } } }})(\sqrt {\sum {X_{2i}^2\sum {X_{3i}^2} } } )}}\) \(\widehat {Cov}(\widehat {{\beta _2}},\widehat {{\beta _3}}) = \frac{{ – 1000\frac{{2500}}{{\sqrt {(1200)(2200)} }}}}{{(1 – {{(\frac{{2500}}{{\sqrt {(1200)(2200)} }})}^2})\sqrt {(1200)(2200)} }} = 0.69252\) |
| Jawaban | b. 0.69252 |