Pembahasan Ujian PAI: A20 – No. 12 – November 2017

PEMBAHASAN

\(E[X] = {M_x}'(t){|_{t = 0}}\) \(E[X] = \)\(\frac{{\partial (\frac{1}{{3(1 – {t_2})}} + \frac{2}{3}{e^{{t_1}}}\frac{2}{{(2 – {t_2})}})}}{{\partial {t_1}}}\) | t₁ = 0, t₂ = 0
\(E[X] = \frac{2}{3}{e^{{t_1}}}\frac{2}{{(2 – {t_2})}}\) | t₁ = 0, t₂ = 0
\(E[X] = \frac{2}{3}\) \(E[{X^2}] = \frac{{{\partial ^2}(\frac{1}{{3(1 – {t_2})}} + \frac{2}{3}{e^{{t_1}}}\frac{2}{{(2 – {t_2})}})}}{{\partial {t_1}^2}}\) | t₁ = 0, t₂ = 0
\(E[{X^2}] = \frac{{\partial (\frac{2}{3}{e^{{t_1}}}\frac{2}{{(2 – {t_2})}})}}{{\partial {t_1}}}\) | t₁ = 0, t₂ = 0
\(E[{X^2}] = \frac{2}{3}{e^{{t_1}}}\frac{2}{{(2 – {t_2})}}\) | t₁ = 0, t₂ = 0
\(E[{X^2}] = \frac{2}{3}\) \(Var[X] = \frac{2}{3} – {\left( {\frac{2}{3}} \right)^2}\) \(Var[X] = \frac{2}{9}\)

Jawaban pada pilihan : D. 2/9