When they ask you to write the gross future loss random variable so you should not write the notations like Ax or (IA)x these notations are used while calculating the reserves, whereas while writing the random variable you should write the symbols like v or kx like they have expressed in examiner's report. let me explain the reason variable means it can take any value suppose the person lives 10 years so accordingly the value kx and V^k is decided so that is why the variable is expressed in such a way so that by putting the different values of v and kx we can know what will be our loss under different cases. for example if the person lives 7 years so company will have different value of loss, if he lives 8 years so company will have different value of loss, so its the random variable which is a tool which helps us to know what will be value of loss under different situations, and that is why the variable is expressed in that way. suppose i adopt the method which you adopted and person lives say 5 years so how the company know the value of loss or profit , if the person lives 5 years since in your method by doing A bar [40] you have considered all the possibilities.
