Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Perhatikan tabel berikut, Cari nilai k sehingga nilai koefisin Korelasi linear tepat nol
| x | 2 | 4 | 7 |
| y | 3 | 5 | k |
- 8
- 3
- 33
- 25
- 41
PEMBAHASAN
| Diketahui | \(n = 3,{\rm{ }}{r_{x,y}} = 0\) |
| Rumus | \({r_{x,y}} = \frac{{n\sum {XY} – \sum X \sum Y }}{{\sqrt {n\sum {{X^2} – {{(\sum X )}^2}} } – \sqrt {n\sum {{Y^2} – {{(\sum Y )}^2}} } }}\) |
| Pembahasan | Karna \(_{x,y} = 0,\) maka \(0 = \frac{{n\sum {XY} – \sum X \sum Y }}{{\sqrt {n\sum {{X^2} – {{(\sum X )}^2}} } – \sqrt {n\sum {{Y^2} – {{(\sum Y )}^2}} } }}\) haruslah \(n\sum {XY} – \sum X \sum Y = 0\) \(\Leftrightarrow 3(6 + 20 + 7k) – (13)(8 + k) = 0\) \(\Leftrightarrow 3(6 + 20 + 7k) = (13)(8 + k)\) \(\Leftrightarrow 78 + 21k = 104 + 13k\) \(\Leftrightarrow k = 3.25\) |
| Jawaban | D. 3.25 |