Reading 8: Probability Concepts - LOS l ～ Q1-2 class, black, style

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1、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)   -12.0.

B)   24.0.

C)   6.0.

D)   -4.9.

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

A)   125.00.

B)   11.18.

C)   120.00.

D)   25.00.

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答案和详解如下：

1、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)   -12.0.

B)   24.0.

C)   6.0.

D)   -4.9.

The correct answer was A)    

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.

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

A)   125.00.

B)   11.18.

C)   120.00.

D)   25.00.

The correct answer was C)

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

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