Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 205 / 1 / b / i / Solution

For points $x_1,\dots ,x_n$ and coefficients $c_1,\dots ,c_n$,The bound $|\hat{\varphi }|\le M$ ensures that this expected value is finite. Symmetry is immediate, so an expected outer product of a random feature map always defines a positive-semidefinite kernel.