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    hey everyone i could do some help with a question i have from a solomon S2 paper i have just tried to do.
    the question paper and answer scheme can be found here. its the solomon paper C question 7 part (d).

    ---
    The random variable Y follows a continuous uniform distribution over the interval [a, b].

    (d) Show by integration that
    E(Y^2) = \frac{(a^2+ab+b^2)}{3}

    Now i can work this out to:
    E(Y^2) = \frac{b^3-a^3}{3(b-a)}
    but in the mark scheme it jumps straight from this to
    E(Y^2) = \frac{(a^2+ab+b^2)}{3}
    i wonder if anyone could show me the steps between these. maybe i am just missing something very simple.

    cheers in advance!
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    hey everyone i could do some help with a question i have from a solomon S2 paper i have just tried to do.
    the question paper and answer scheme can be found here. its the solomon paper C question 7 part (d).

    ---
    The random variable Y follows a continuous uniform distribution over the interval [a, b].

    (d) Show by integration that
    E(Y^2) = \frac{(a^2+ab+b^2)}{3}

    Now i can work this out to:
    E(Y^2) = \frac{b^3-a^3}{3(b-a)}
    but in the mark scheme it jumps straight from this to
    E(Y^2) = \frac{(a^2+ab+b^2)}{3}
    i wonder if anyone could show me the steps between these. maybe i am just missing something very simple.

    cheers in advance!
    Simply took a factor of (b-a) out of the expression

     b^3 - a^3 = (b - a)(a^2 + ab + b^2)

    Exactly how you're supposed to spot this in an exam though is a mystery, unless its a 'show that' question - at least it should only be one mark lost if it wasn't spotted!
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    (Original post by spread_logic_not_hate)
    Simply took a factor of (b-a) out of the expression

     b^3 - a^3 = (b - a)(a^2 + ab + b^2)

    Exactly how you're supposed to spot this in an exam though is a mystery, unless its a 'show that' question - at least it should only be one mark lost if it wasn't spotted!
    thanks for the help, i didnt notice that.
    had this exam today, so glad i don't have to think about it anymore anyway lol.
 
 
 
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