grandes-ecoles 2020 Q19

grandes-ecoles · France · centrale-maths2__mp Continuous Probability Distributions and Random Variables Verification of Probability Measure or Inner Product Properties

For all $k \in \mathbb{N}^*$, we set $g_k(x) = \sqrt{2}\sin(k\pi x)$. Show that the family of vectors $(g_k)_{k \in \mathbb{N}^*}$ is orthonormal.

For all $k \in \mathbb{N}^*$, we set $g_k(x) = \sqrt{2}\sin(k\pi x)$.
Show that the family of vectors $(g_k)_{k \in \mathbb{N}^*}$ is orthonormal.