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Exercise 4 (MATH 4200). Suppose that Xk has a probability density function f(x) so that f(x)...

Exercise 4 (MATH 4200). Suppose that Xk has a probability density function f(x) so that f(x) > 0 for all x.

Prove that

G(c) = E[Xk Xk ≥ c]P(Xk ≥ c) + µk+1P(Xk ≤ c)

is maximal is maximal for c = µk+1.

(This means the optimal strategy is to take γk = µk+1.)

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orchestra answered 2 years ago
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