# 2020_III_11_Probability

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Solution

Q11 STEP3 2020.pdf (1.9 MB)

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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 didnâ€™t use (i) in (ii).

I didnâ€™t think showing that Z had all the required properties to use part (i) was â€śworth itâ€ť to get an expression for \mathbb E[Z^2], when it doesnâ€™t actually â€śdo muchâ€ť 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 donâ€™t think youâ€™re missing something. I just got the feeling they â€śwantedâ€ť it to be done using part (i) because the function so â€śobviouslyâ€ť had the required properties, and itâ€™s a fairly boring result to have derived. STEP is so often about reading between the lines to try something that if I think Iâ€™m being told to do something I go along with it (who am I to know any betterâ€¦). That said, both papers this year seemed a little odd to me. Like Q10, which seemed to start â€śdo the SHM thingâ€ť. 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 donâ€™t envy the people that write these papers.

I agree, I was expecting (i) to give some sort of â€śa haâ€ť moment to the integral of \mathbb E[Z^2], but maybe they couldnâ€™t find a good enough example since itâ€™s easy enough to work \mathbb E[Z^2] directly here.

I think in this case following the â€śintended methodâ€ť 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.