Pea-nuckle war!

So its that time of year, and im looking at some prev exams (April '05 to be exact)

Q11 -10 marks
-i challenge anyone to complete this question in 20minues (i.e.~ 3hrs/100marks*10 marks)
if you are willing and able to complete this task you are one step away from pea-nuckle champion of the world!
to support this claim here are some of the basic facts:
1. you must have extreme digit flexibility, able to write square brackets (for select mortality) and superscript text in one smooth flick of the wrist.
2. you must be able to use 'the force' predicting your opponent (in this case a monthly term assurance) next move/value
3. you must be able to do 1 & 2 together at the same time (or else you will enevitably run out of time.

if you think you are made of the right stuff, reply to this threat. you now doubt have mastered the technique over many years and may have a few quick tips.

p.s. i have tried the yoga technique of 'the handstand.' This attacks both skills, the blood rushed to my brain, and my hands get a work out. but in the in the words of jake the mus* i fear im working on "too much strength and not enough speed"

*see the movie once were warriors

my next questions may have something to do with too much blood in my brain (from all those handstands)...

Q12.i. LHS = RHS??? i get LHS ~=RHS. someones got to explain to me how one can go from a function based on a continous life to a function based on a discrete life. i know its just a simple matter of turning a intergral into a sum, but with only ='s???

Q12.ii. i managed to work this one out, but surprise, surprise i got a different answer from the examiners report. could someone explain to me if there is a difference between the variance of a present value and the variance of an expected present value i.e. Var(X) vs Var(E[X]) i thought i took CT2 and i thought there was a whole section on the do's and donts about these things.. but then again those handstands may be deluding me into false memories!

any explanation of these facts would be much appreciated.

 

Var(E(X)) = 0, since expectation is simply a number and has no variance.

 

Var(E[X])?

if Var(E[X]) = 0 which makes alot of sense why does examiners report differ?

 

not looked at the question - but if E[X] is unknown then you might model E[X] with a distribution and hence it would have a variance. Might be completely wrong though.