Define MISE. Show that the selection of (c_{j}) as [ c_{j}=frac{1}{T} int_{0}^{T} f(t) varphi_{j}(t) mathrm{d} t ]

Question:

Define MISE. Show that the selection of \(c_{j}\) as

\[
c_{j}=\frac{1}{T} \int_{0}^{T} f(t) \varphi_{j}(t) \mathrm{d} t
\]

reduces MISE to a minimum.

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