3 Solve Dual Analytically A random variable is known to have 1000 possible realizations §1, ..., $1000 such that 0 < L =

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3 Solve Dual Analytically A Random Variable Is Known To Have 1000 Possible Realizations 1 1000 Such That 0 L 1 (53.53 KiB) Viewed 83 times

3 Solve Dual Analytically A random variable is known to have 1000 possible realizations §1, ..., $1000 such that 0 < L = &1 ≤ &2 ≤ ... < €999 ≤ $1000 = U. It is known that the second moment is at least o², that is E[§²] ≥ 0² (with L² ≤ 0² ≤ U²). The probability distribution, i.e., pį = Pr[§ = $i] for i = 1, ..., 10000 is unknown. Use linear programming to prove that the expected value of έ is at least o² + UL U + L Hint: Write an LP with p; as variables. Take the dual of the LP, and solve the dual (analytically) to show the desired result.