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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2024

Paper 4

The identity
$$
\frac1n\sum_{i=1}^n(X_i-\bar X_n)^2
=\frac1n\sum_{i=1}^nX_i^2-\bar X_n^2
$$
and the weak law applied to $X_i$ and $X_i^2$ give convergence in probability to
$$
\boxed{\mathbb EX_1^2-\mu^2=\sigma^2.}
$$


Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 28L / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 28L / a / Solution

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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 28L / a / Solution

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