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Calculating Expected Value and Variance of Random Variables

This quiz focuses on understanding the calculations of expected value and variance of random variables. Given the provided information, we calculate E[X] as 37 and Var[X] as 1701. Additionally, we explore the random variables Y and Z, where E[Y] is 0.2, Var[Y] is 0.1, E[Z] is 0.1, and Var[Z] is 0.1. We calculate E[Y + Z] to find it equals 0.3 and Var[2Y] as 0.4. This exercise reinforces concepts in probability theory and statistics.

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Calculating Expected Value and Variance of Random Variables

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  1. Quiz 10.18.2012 • Given the information above calculate: • E[X] = 30 + 7 = 37 • Var[X] = 510.3+1190.7 = 1701 (bonus) • Let Y and Z be random variables. Let E[Y] = 2, Var[Y] = 1, E[Z] = 1, and Var[Z] = 1. Find: • E[Y + Z] = E[Y] + E[Z] = 2 + 1 = 3 • Var[2Y] = 22Var[Y] = 22(1) = 4

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