Reading 8: Probability Concepts-LOS m 习题精选 2011, function, interpret, border

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Session 2: Quantitative Methods: Basic Concepts
Reading 8: Probability Concepts

LOS m: Calculate and interpret covariance given a joint probability function.

 

 

Given P(X = 20, Y = 0) = 0.4, and P(X = 30, Y = 50) = 0.6, then COV(XY) is:

A) 125.00.

B) 25.00.

C) 120.00.

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The expected values are: E(X) = (0.4 × 20) + (0.6 × 30) = 26, and E(Y) = (0.4 × 0) + (0.6 × 50) = 30. The covariance is COV(XY) = (0.4 × ((20 ? 26) × (0 ? 30))) + ((0.6 × (30 ? 26) × (50 ? 30))) = 120.

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Given P(X = 2, Y = 10) = 0.3, P(X = 6, Y = 2.5) = 0.4, and P(X = 10, Y = 0) = 0.3, then COV(XY) is:

A) 24.0.

B) -12.0.

C) 6.0.

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The expected values are: E(X) = (0.3 × 2) + (0.4 × 6) + (0.3 × 10) = 6 and E(Y) = (0.3 × 10.0) + (0.4 × 2.5) + (0.3 × 0.0) = 4. The covariance is COV(XY) = ((0.3 × ((2 ? 6) × (10 ? 4))) + ((0.4 × ((6 ? 6) × (2.5 ? 4))) + (0.3 × ((10 ? 6) × (0 ? 4))) = ?12.