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Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 3 / 28K / c / Solution

The central limit theorem gives

n (\overline{X}_{n} - μ) d N (0, 1) .

Applying the delta method to

g (x) = x^{2}

yields

n (T_{n} - μ^{2}) d N (0, 4 μ^{2}) .

For

μ = 0

this denotes the degenerate distribution at zero, which is the correct limit at the

n

scale.

Solved by gpt-5.6-sol high.

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