2020_III_11_Probability

2020_III_11_Probability

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Solution

Q11 STEP3 2020.pdf (1.9 MB)

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:muscle:

When I worked through this question for the TSR thread - I found (i) and (ii) to be a bit odd to include together and when I spoke to some people they asked me why I didn’t use (i) in (ii).

I didn’t think showing that Z had all the required properties to use part (i) was “worth it” to get an expression for \mathbb E[Z^2], when it doesn’t actually “do much” to wittle down the demand, if anything. Working the integral directly (using the standard integral for \mathbb E[f(X)]) is actually quicker. Am I missing something?

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I don’t think you’re missing something. I just got the feeling they “wanted” it to be done using part (i) because the function so “obviously” had the required properties, and it’s a fairly boring result to have derived. STEP is so often about reading between the lines to try something that if I think I’m being told to do something I go along with it (who am I to know any better…). That said, both papers this year seemed a little odd to me. Like Q10, which seemed to start “do the SHM thing”. It felt like questions had been rewritten several times, and potentially lost their initial clean look, perhaps because they were too difficult to start with, or too easy for 20 marks. I certainly don’t envy the people that write these papers.

I agree, I was expecting (i) to give some sort of “a ha” moment to the integral of \mathbb E[Z^2], but maybe they couldn’t find a good enough example since it’s easy enough to work \mathbb E[Z^2] directly here.

I think in this case following the “intended method” sinks a bit more time with pretty much no payoff, which might have aided people who were panicked in the time pressure. (but I guess stats questions were never that popular in the first place)

Just struck me as odd, is all.