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random cubic polynomial

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November 15, 2009
algebrapolynomialprobabilityexpected value

Problem Statement

Let y0 y_0 be chosen randomly from {0,50} \{0, 50\}, let y1 y_1 be chosen randomly from {40,60,80} \{40, 60, 80\}, let y2 y_2 be chosen randomly from {10,40,70,80} \{10, 40, 70, 80\}, and let y3 y_3 be chosen randomly from {10,30,40,70,90} \{10, 30, 40, 70, 90\}. (In each choice, the possible outcomes are equally likely to occur.) Let P P be the unique polynomial of degree less than or equal to 3 3 such that P(0) \equal{} y_0, P(1) \equal{} y_1, P(2) \equal{} y_2, and P(3) \equal{} y_3. What is the expected value of P(4) P(4)?
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