Functions of a DRV

Functions of a DRV Quiz

Spec SA5 · AQA A-Level Further Maths: Quiz

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  1. 1. X=1X=1 or 33 with probability 0.50.5 each. Find E(X2)E(X^2).

    • A. 44
    • B. 55
    • C. 1010
    • D. 22

  2. 2. X=1X=1 or 22 with probability 0.50.5 each. Find E(1X)E\left(\frac1X\right).

    • A. 23\frac23
    • B. 1.51.5
    • C. 0.50.5
    • D. 0.750.75

  3. 3. Var(X−1)=0.09\mathrm{Var}(X^{-1})=0.09. Find Var(6X−1)\mathrm{Var}(6X^{-1}).

    • A. 3.243.24
    • B. 0.540.54
    • C. 0.090.09
    • D. 3636

  4. 4. E(X3)=12.3E(X^3)=12.3. Find E(5X3)E(5X^3).

    • A. 17.317.3
    • B. 12.312.3
    • C. 61.561.5
    • D. 6.156.15

  5. 5. Which statement is true in general?

    • A. E(1/X)=1/E(X)E(1/X)=1/E(X)
    • B. E(X2)≥[E(X)]2E(X^2)\ge[E(X)]^2
    • C. E(g(X))=g(E(X))E(g(X))=g(E(X)) for any gg
    • D. E(X2)=[E(X)]2E(X^2)=[E(X)]^2

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