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Combining Random Variables

AP Statistics· difficulty 4/5

X and Y are independent with means 20 and 15, SDs 3 and 4.

X mean = 20 SD = 3 Y mean = 15 SD = 4 Find X - Y

What is the mean and SD of X - Y?

  • A

    mean 5, SD 7

  • B

    mean 5, SD 5

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  • C

    mean 35, SD 5

  • D

    mean 5, SD 1

Explanation

E(X-Y) = 20-15 = 5. Var(X-Y) = 9+16 = 25. SD = 5. (Variances always add for independence.)

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