Hey all i have been looking at this, and im struggling to find where im going wrong, or if i even am. Here is the question, with my attempt.

Part (iii) (a) is the most difficult for me.

(ii) I got [latex] \alpha = \dfrac{1}{500} [/latex]

(iii)

(a)This is the bit im most concerned about.

$\displaystyle [1-(1-X_1)(1-X_2)(1-X_3)]\cdot[1-(1-X_4)] $

$\displaystyle [1-(1-R_1(t))(1-R_2(t))(1-R_3(t))]\cdot[1-(1-R_4(t))] $

Am i correct or should i be writing if so why, or why not? The independance is whats confusing me.

$\displaystyle [1-(X_1)(X_2)(X_3)]\cdot[1-(X_4)] $

$\displaystyle [1-(R_1(t))(R_2(t))(R_3(t))]\cdot[(1-R_4(t))] $

(b) I just then sub $\displaystyle R(t) = e^\frac{-t}{500} $, and then expand and integrate.