=+20. Let Bnf(x) = E[f(Sn/n)] denote the Bernstein polynomial of degree n approximating f(x) as discussed in
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=+20. Let Bnf(x) = E[f(Sn/n)] denote the Bernstein polynomial of degree n approximating f(x) as discussed in Example 3.5.1. Prove that
(a) Bnf(x) is linear in f(x),
(b) Bnf(x) ≥ 0 if f(x) ≥ 0,
(c) Bnf(x) = f(x) if f(x) is linear,
(d) Bnx(1 − x) = n−1 n x(1 − x).
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