Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 207 / 3 / b / Solution

Set $x_{\ast }=0.5$ in the Gaussian process regression posterior and compute $m_{\ast }$ and $v_{\ast }$ as in part a. Standardization of a normal random variable then giveswhere $\Phi$ is the standard normal cumulative distribution function.