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    (Original post by Zacken)
    Once you know that, life becomes a hell of a lot easier, that's how you can derive distributions of the mean for n samples.

    You take n samples \sum_{i}^n X_i then scale it by \frac{1}{n} so we have:

    \displaystyle 

\begin{equation*}E(\bar{X}) = E\left(\frac{X_1 + \cdots X_n}{n}\right) = \frac{1}{n}(\mu + \cdots + \mu) = \frac{1}{n}(n\mu) = \mu \end{equation*}

    So the expected value of the mean is the same as the expect value of the distribution.

    You can do something similar with variance:

    \displaystyle 

\begin{equation*}\text{Var}{\bar  {X}} = \text{Var}\left(\frac{X_1 + \cdots X_n}{n}\right) = \frac{1}{n^2}(\sigma^2 + \cdots + \sigma^2) = \frac{n\sigma^2}{n^2} = \frac{\sigma^2}{n}\end{equation*  }

    This shows that the more samples you take, the smaller your variance becomes - which is what we expect.
    I see so you cant do
    Var(x/n +x2/n etcc) right you take factors out first if not grouped together you keave em right. I see. Any you guys done th 2015 s3 uk paper yet?


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    (Original post by physicsmaths)
    Any you guys done th 2015 s3 uk paper yet?

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    yep are you going to ask about Q5?
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    (Original post by aymanzayedmannan)
    DylanJ42 has
    btw remember the little thing i was unsure about in that test, it how it would determine 87UMS or 90UMS? well the teacher said it was fine so 90UMS yay :laugh:
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    (Original post by DylanJ42)
    btw remember the little thing i was unsure about in that test, it how it would determine 87UMS or 90UMS? well the teacher said it was fine so 90UMS yay :laugh:
    Damn! That was a hard paper, too - well done
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    Could anyone explain question 3d please https://drive.google.com/folderview?...&usp=drive_web can't really get my head around what it's actually saying? Thanks
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    (Original post by aymanzayedmannan)
    Damn! That was a hard paper, too - well done
    PRSOM :dontknow:

    thank you :cute: 66 raw though, so boundaries reflected the difficulty
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    (Original post by DylanJ42)
    yep are you going to ask about Q5?
    I have not done it yet. Was it a ch 1 question that screwed everyone over?


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    (Original post by physicsmaths)
    I have not done it yet. Was it a ch 1 question that screwed everyone over?


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    It was indeed, combining dependent random variables rather than independent ones though. 6 marks down the drain

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    (Original post by DylanJ42)
    It was indeed, combining dependent random variables rather than independent ones though. 6 marks down the drain

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    Damn how the **** would that work 😂
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    (Original post by physicsmaths)
    Damn how the **** would that work 😂
    It's not that bad if you think about it..shame I thought about it too much and got the easy ones wrong instead
    Actually looking back at the paper it seems almost "obvious", exam pressure can do strange things
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    (Original post by economicss)
    Could anyone explain question 3d please https://drive.google.com/folderview?...&usp=drive_web can't really get my head around what it's actually saying? Thanks
    If you still need help it's basically just "how does combining the adults and children affect the error relative to the errors for each group"
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    (Original post by physicsmaths)
    Damn how the **** would that work 😂
    I'll not spoil it for you, but know the derivations (I guess) for the E(X) and Var(X) formula and how they work

    As 13 1 20... said it's not bad at all in hindsight, I think you'll kick yourself if you don't get it hahaha (no pressure)

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    (Original post by 13 1 20 8 42)
    If you still need help it's basically just "how does combining the adults and children affect the error relative to the errors for each group"
    Thank you, I understand the first mark in the mark scheme but for the second mark it says the difference in the means will be quite large ( so variations from the overall mean will be large giving a larger overall se) and I'm not really sure how you can get this from the values?
    Thanks
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    (Original post by economicss)
    Thank you, I understand the first mark in the mark scheme but for the second mark it says the difference in the means will be quite large ( so variations from the overall mean will be large giving a larger overall se) and I'm not really sure how you can get this from the values?
    Thanks
    Basically the point is that for both children and adults, their weight will be further away from the mean than it would have been in their own group and so you expect larger error overall. Although the error from adults in the combined group might still be a tad smaller than the error from children in their own group, note that as there are so many more children than adults it seems pretty much certain that the average error will be larger overall. I don't know if you can say it for sure/it might take a little more effort to prove, but I think you're just expected to see that that's probably the case.
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    (Original post by 13 1 20 8 42)
    Basically the point is that for both children and adults, their weight will be further away from the mean than it would have been in their own group and so you expect larger error overall. Although the error from adults in the combined group might still be a tad smaller than the error from children in their own group, note that as there are so many more children than adults it seems pretty much certain that the average error will be larger overall. I don't know if you can say it for sure/it might take a little more effort to prove, but I think you're just expected to see that that's probably the case.
    Thanks!
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    https://771a1ec81340d97ae9ed29694f73...XZCVmc/CH3.pdf On question 2b of exercise 3a, could anyone explain how you do it please as I can't seem to get the answer on solutions bank. Thanks
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    (Original post by economicss)
    Thanks!
    Looking back I think I mixed up things a lot in that actually lol. If you take any given adult, you expect the error to be greater for them in the combined group than in their own group since the mean is further away, and if you take any given child, you expect the error to on average exceed the error for adults in their own group, since the combined mean is probably less close to each child's weight than the adult mean is to each adult's weight...think that's okay reasoning..
    tbh I think I missed out on this mark in the exam, I lost 5 raw and accounted for another 4
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    (Original post by SeanFM)
    :woo:

    And S3 wouldn't be S3 without it clashing with another module, and this year it clashes with C2. :woo: :party:

    Here are some resources, inspired by resources from the thread of the previous year.

    Madasmaths - awesome website for loads of things for all of your exams, with a few topics that come up in S3.

    PhysicsAndMathsTutor - link to loads of useful things.

    FMSP revision page - some videos to watch about the specification and a specific set of exam questions.

    If there is demand I can start an S4 thread as well..!

    And if you have any questions, fire away!
    Could you make an S4 thread aswell?

    Tag me in it please if you do.


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    (Original post by physicsmaths)
    Could you make an S4 thread aswell?

    Tag me in it please if you do.


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    Are you doing AS or A2 AFM?
 
 
 
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