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# S2 question help watch

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1. 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

Now i can work this out to:

but in the mark scheme it jumps straight from this to

i wonder if anyone could show me the steps between these. maybe i am just missing something very simple.

2. 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.

Simply took a factor of (b-a) out of the expression

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

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.

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Updated: January 19, 2010
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