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    Papers seem quite regurgitative:

    Random Variables
    Confidence intervals/unbaised estimators
    Contingecy Table
    Sampling - probably stratified
    spearman's rank
    poisson distribution
    CLT/2 independent ND

    Seems the general trend of every paper tbh
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    (Original post by L'Evil Wolf)
    Papers seem quite regurgitative.
    Every A-Level module ever.
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    (Original post by Zacken)
    Every A-Level module ever.
    Yeah haha.

    btw if you and others havent checked this out already;

    http://drfrostmaths.com/page.php?page=21

    good site, especially for S3 theory.
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    (Original post by L'Evil Wolf)
    Papers seem quite regurgitative:

    Random Variables
    Confidence intervals/unbaised estimators
    Contingecy Table
    Sampling - probably stratified
    spearman's rank
    poisson distribution
    CLT/2 independent ND

    Seems the general trend of every paper tbh
    a question to s3 is that it can be taught within days and one can do papers and get A's. ridiculously easy material to get a hang of.
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    (Original post by physicsmaths)
    a question to s3 is that it can be taught within days and one can do papers and get A's. ridiculously easy material to get a hang of.
    I agree, the concept of the 2 tailed test used prevelantly in chapter 5 should be used if possible in Chapter 4 with chi squared.

    Shame, we don't do wilcoxon, f,t distributions, not even in yates correction is used aha
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    is there any particularly hard s3 paper except from the june 15 one ??
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    Could someone please explain how and why to perform the variance calculation on part (d) of Q5 2015?
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    (Original post by Euclidean)


    Could someone please explain how and why to perform the variance calculation on part (d) of Q5 2015?
    Express U-bar in terms of what it actually means. i.e. U-bar = 0.2(U_1 + ... + U_5).

    By the way, did you manage to find your hard papers?
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    (Original post by Euclidean)


    Could someone please explain how and why to perform the variance calculation on part (d) of Q5 2015?
    Well the how has been answered...but as to why, have you answered c? Essentially, it's all about dependence
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    (Original post by Ayman!)
    Express U-bar in terms of what it actually means. i.e. U-bar = 0.2(U_1 + ... + U_5).

    By the way, did you manage to find your hard papers?
    Nah I think S3 is pretty standard except for this one. I fluffed up this part (d) though so lost 5 marks there...

    I understand writing the mean in terms of 0.2(sum) but I don't understand where this variance calculation has come from...

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    (Original post by 13 1 20 8 42)
    Well the how has been answered...but as to why, have you answered c? Essentially, it's all about dependence
    I answered (c):
    The variance combinations formula only applies if the samples are independent, which is not necessarily true for any sample hence the assumption of the same variance as in part (b) cannot be made
    I gave myself that mark
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    (Original post by Euclidean)
    Nah I think S3 is pretty standard except for this one. I fluffed up this part (d) though so lost 5 marks there...

    I understand writing the mean in terms of 0.2(sum) but I don't understand where this variance calculation has come from...

    It's just the normal combination of variables. Each of the Ui has variance sigma^2, and when combining you use the rule (here extending to more than two variables of course) Var(aX + bY) = a^2Var(X) + b^2Var(Y)
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    (Original post by Euclidean)
    Nah I think S3 is pretty standard except for this one. I fluffed up this part (d) though so lost 5 marks there...

    I understand writing the mean in terms of 0.2(sum) but I don't understand where this variance calculation has come from...

    Well, what does \mathrm{Var\left ( F \right )}= \mathrm{Var\left ( U_{1}-\bar{U} \right )}= \mathrm{Var\left ( \frac{5U_{1}-U_{1}-\cdots -U_{5}}{5} \right )} compute to? Remember that we can't directly use Var(aX + bY) = Var(aX) + Var(bY) on Var(U - U-bar) because U and U-bar are not independent.
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    (Original post by 13 1 20 8 42)
    Var(aX + bY) = a^2Var(X) + b^2Var(Y)
    Doesn't this only work for independent variables? :cry2:

    (Original post by Ayman!)
    Well, what does \mathrm{Var\left ( F \right )}= \mathrm{Var\left ( U_{1}-\bar{U} \right )}= \mathrm{Var\left ( \frac{5U_{1}-U_{1}-\cdots -U_{5}}{5} \right )} compute to? Remember that we can't use Var(aX + bY) = Var(aX) + Var(bY) on Var(U - U-bar) because U and U-bar are not independent.
    I honestly do not know

    \displaystyle \mathrm{Var\left(\dfrac{4U_1 - U_2 - U_3 - U_4 - U_5}{5}}\right)}

    How should I evaluate this for any sample?

    I think I just don't understand what conditions the formulae require properly...
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    Name:  Screen Shot 2016-05-23 at 15.32.23.png
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    I dont really get part c of this question, the MS said 2 x "their alpha " + 3
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    (Original post by Ayman!)
    Remember that we can't directly use Var(aX + bY) = Var(aX) + Var(bY) on Var(U - U-bar) because U and U-bar are not independent.
    I think I understand your statement now.

    We can't go straight into Var(aX + bY) = Var(aX) + Var(bY) but we can apply it to the individual X_i's right?
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    (Original post by anndz3007)
    Name:  Screen Shot 2016-05-23 at 15.32.23.png
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    I dont really get part c of this question, the MS said 2 x "their alpha " + 3
    alpha is the mean you calculate and the +3 is cause if you look at the question at the top, the max would be 2a + 3 hence that's what they've done for the max value.
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    (Original post by Euclidean)
    I think I understand your statement now.

    We can't go straight into Var(aX + bY) = Var(aX) + Var(bY) but we can apply it to the individual X_i's right?
    Apologies for the slow replies, my 'tex is not that good. But yes - that is precisely what I meant. You can't jump straight into that because the mean is dependent on the individual Xis, but each Xi isn't dependent on each other - they're all independent units. That's why we can go \mathrm{Var\left ( \frac{4U_{1}-U_{2}-\cdots -U_{5}}{5} \right )} = \frac{1}{25} \left[ \mathrm{ Var\left (4U_{1} \right )+Var\left ( U_{2} \right )+\cdots +Var\left ( U_{5} \right ) } \right]. That's my interpretation of what's going on here, at least. I'm also curious as to what 13 1 20 8 42 says.
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    (Original post by Euclidean)
    Doesn't this only work for independent variables? :cry2:
    (Original post by Ayman!)
    Apologies for the slow replies, my 'tex is not that good. But yes - that is precisely what I meant. You can't jump straight into that because the mean is dependent on the individual Xis, but each Xi isn't dependent on each other - they're all independent units. That's why we can go \mathrm{Var\left ( \frac{4U_{1}-U_{2}-\cdots -U_{5}}{5} \right )} = \frac{1}{25} \left[ \mathrm{ Var\left (4U_{1} \right )+Var\left ( U_{2} \right )+\cdots +Var\left ( U_{5} \right ) } \right]. That's my interpretation of what's going on here, at least. I'm also curious as to what 13 1 20 8 42 says.
    Yeah it's basically that the individual Ui are independent so the point of expressing the mean in terms of them is that you can then use the standard expectation algebra
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    (Original post by coolguy123456)
    alpha is the mean you calculate and the +3 is cause if you look at the question at the top, the max would be 2a + 3 hence that's what they've done for the max value.
    lol thank you, i thought it's a new formula, didnt notice the max value in the distribution.
 
 
 
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