Did you write the question correctly? Given your answer, it looks likes you were asked to compute . Anyway, your answer equals , i.e. you forgot to divide the result by .

(By the way, it is usually advisable to write small in the integral because it is not exactly the same as , without further precision)

Always start by writing what these conditional expectations stand for; in this case, it is . Can you see why I said that?b)

OK, for a start.c)

I don't get it; you want . Isn't it just the same as ?d) compute with rates and

based on my book the probabilistic minimum of is just (no proof was given) so in this case it would be also I would like to show that is the case, with 2 variable. I thought it would be:

but that give me 1 and

another way I considered was

I finally considered but I don't know what to pick since they are both different.