Question

Let Z be a discrete random variable (for example, random demand for a product or service) taking values on the set {0, 1, 2, 3, 4, 5}. We have limited information about the behavior of Z. We do not know its exact probability distribution. However, we do know that Z has an expected value of 3, and that each realization of Z happens with a probability of at least 0.10. We also know that Pr(Z ≥ 4) is at least 0.4. (a) Formulate two Linear Programming problems that will help provide an upper bound and a lower bound on the variance of Z. (b) Write the LPs so that they are "MATLAB ready", i.e., max/min c · x s.t. Ax ≤ b, Aeq · x = beq, x ≥ 0. Clearly define A, Aeq, b, beq, and c. (c) Use Excel to solve the two problems.

          Let Z be a discrete random variable (for example, random demand for a product or service) taking values on the set {0, 1, 2, 3, 4, 5}. We have limited information about the behavior of Z. We do not know its exact probability distribution. However, we do know that Z has an expected value of 3, and that each realization of Z happens with a probability of at least 0.10. We also know that Pr(Z ≥ 4) is at least 0.4.

(a) Formulate two Linear Programming problems that will help provide an upper bound and a lower bound on the variance of Z.

(b) Write the LPs so that they are "MATLAB ready", i.e., max/min c · x s.t. Ax ≤ b, Aeq · x = beq, x ≥ 0. Clearly define A, Aeq, b, beq, and c.

(c) Use Excel to solve the two problems.

Added by Meghan G.

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