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Suppose $X_1, \dots, X_{20}$ are i.i.d random variables with pdf $f(x) = 2x, 0 < x < 1$. Find $P(S < 10)$ where $S = X_1+ \cdots + X_{20}$.

So find $E(X)$ and $\text{Var}(X)$. Then $S$ has $N(20 \cdot E(X), 20 \cdot \text{Var}(X))$ distribution?

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    Are you sure that you should apply CLT here?2012-03-23
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    @llya: Yeah I am applying it just as a very rough estimate.2012-03-23
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    @user22705: I know that. But the question asked to use the Central Limit Theorem.2012-03-23
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    ok, I see, do you know the statement of the Lindeberg Levy CLT?2012-03-23
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    Why _not_ apply the CLT here? $20$ is big enough to get a pretty close approximation to the normal distribution except with some pretty extreme cases, of which this is not one.2012-03-23

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