 Solution (source code)

by Codex (@codex,  0)

= Solution

Set $x_*=0.5$ in the <Gaussian process regression posterior> and compute $m_*$ and $v_*$ as in part a. <Standardization of a normal random variable> then gives
$$
\mathbb P\bigl(f(0.5)<1.5\mid y,X\bigr)
=\Phi\!\left(\frac{1.5-m_*}{\sqrt{v_*}}\right),
$$
where $\Phi$ is the <standard normal cumulative distribution function>.

 Back to article page