28 April, 2024

HomeBlogEdukasiAktuariaPembahasan Ujian Profesi Aktua...A50 - Metoda StatistikaPembahasan Ujian PAI: A50 &#82...

Pembahasan Ujian PAI: A50 – No. 2 – Juni 2015

3 September 2019

by Fery Widhiatmoko

with one comment

A50 - Metoda Statistika Aktuaria Edukasi Pembahasan Ujian Profesi Aktuaris (Persatuan Aktuaris Indonesia / PAI)

Pembahasan Soal Ujian Profesi Aktuaris

Institusi	:	Persatuan Aktuaris Indonesia (PAI)
Mata Ujian	:	Metoda Statistika
Periode Ujian	:	Juni 2015
Nomor Soal	:	2

SOAL

Diketahui survival function dari \(X\) adalah \(\begin{array}{*{20}{c}} {S\left( x \right) = {e^{ – x}}\left( {x + 1} \right),}&{x \ge 0} \end{array}\)

Tentukan \(E\left[ X \right]\)

0,25
1
0,5
2
0

Kunci Jawaban & Pembahasan

One Response

Pembahasan Ujian PAI: A50 - No. 3 - Juni 2015 - Data Polis 3 February 2023 at 14:29

[…] Berdasarkan soal nomor 2 […]

Log in to Reply

Diketahui	\(\begin{array}{*{20}{c}} {S\left( x \right) = {e^{ – x}}\left( {x + 1} \right),}&{x \ge 0} \end{array}\)
Rumus yang digunakan	\(E\left[ X \right] = \int\limits_0^\infty {S\left( x \right)dx} \)
Proses pengerjaan	\({E\left[ X \right] = \int\limits_0^\infty {{e^{ – x}}\left( {x + 1} \right)dx} }\) misal \({u = – x \Leftrightarrow du = – dx}\) \({E\left[ X \right] = \int\limits_0^\infty {{e^u}\left( {u – 1} \right)du} }\) misal \({v = {e^u} \Leftrightarrow dv}\) \(= {e^u}du\) \(E\left[ X \right] = \int\limits_0^\infty {\left[ {\ln \left( v \right) – 1} \right]dv} \) \(E\left[ X \right] = \left. {\left[ {v\ln \left( v \right) – v – v} \right]} \right\|_0^\infty = \left. {\left[ {v\ln \left( v \right) – 2v} \right]} \right\|_0^\infty \) \(E\left[ X \right] = \left. {\left[ {{e^{ – x}}\ln \left( {{e^{ – x}}} \right) – 2{e^{ – x}}} \right]} \right\|_0^\infty \) \(E\left[ X \right] = 2\)
Jawaban	d. 2

Trending Topic

One Response

Leave A Comment Cancel reply

Most View

Random Post