Residual sum of squares in a normal sample

For independent

N (μ, σ^{2})

\sum_{i} (X_{i} - \overset{ˉ}{X})^{2} / σ^{2}

has the

χ_{n - 1}^{2}

distribution.

Table of contents
- Chi-square central limit theorem Residual sum of squares in a normal sample

Chi-square central limit theorem

If

Q_{m} \sim χ_{m}^{2}

, then

(Q_{m} - m) / 2 m

converges in distribution to

N (0, 1)

.

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Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 44 / 4 / Solution

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