Pembahasan Ujian PAI: A20 – No. 30 – Mei 2017

PEMBAHASAN

Misalkan:
X ialah banyak orang yang meninggal
B ialah besar pembayaran polis

\(B = \left\{ \begin{array}{l} 0,x = 0\\ 100.000,x = 1\\ k,x = 2 \end{array} \right.\) \(P(X \ge 1) = 0,1\) \(P(X = 1) = 0,08\) \(P(X = 2) = 0,1 – 0,08 = 0,02\) \(P(X = 0) = 1 – 0,1 = 0,9\) \({\sigma _B} = 74.000\)

\(Var[B] = E[{B^2}] – E{[B]^2}\) \({\sigma _B}^2 = (0 + {100.000^2}(0,08) + {k^2}(0,02)) – {(0 + 100.000(0,08) + k(0,02))^2}\) \(5.476.000.000 = (800.000.000 + 0,02{k^2}) – {(8.000 + 0,02k)^2}\) \(4.647.000.000 = 0,02{k^2} – 64.000.000 – 320k – 0,0004{k^2}\) \(0,0196{k^2} – 320k – 4.740.000.000 = 0\) \(k = 500.000\) \(k = – 483.606\) \(k > 0\) \(k = 500.000\) \(E[B] = 0 + 100.000(0,08) + 500.000(0,02)\) \(E[B] = 18.000\)

Jawaban: a. 18.000