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Combining Random Variables

AP Statistics· difficulty 4/5

X and Y are independent with Var(X)=4, Var(Y)=9. T = 2X + 3Y.

X Var = 4 Y Var = 9 T = 2X + 3Y, indep.

What is Var(T)?

  • A

    13

  • B

    30

  • C

    25

  • D

    97

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Explanation

Var(T) = 4<em>Var(X) + 9</em>Var(Y) = 4(4) + 9(9) = 16 + 81 = 97.

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