Distributions and expectation of DRVs

Distributions and expectation of DRVs Quiz

Spec SA1–SA4 · AQA A-Level Further Maths: Quiz

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  1. 1. P(X=x)=kxP(X=x)=kx for x=1,2,3x=1,2,3. Find kk.

    • A. 13\frac13
    • B. 16\frac16
    • C. 114\frac1{14}
    • D. 12\frac12

  2. 2. XX takes 0,1,20,1,2 with probabilities 0.5,0.3,0.20.5,0.3,0.2. Find E(X)E(X).

    • A. 0.70.7
    • B. 11
    • C. 0.50.5
    • D. 0.90.9

  3. 3. E(X)=3E(X)=3 and E(X2)=10E(X^2)=10. Find Var(X)\mathrm{Var}(X).

    • A. 77
    • B. 11
    • C. 9191
    • D. 10\sqrt{10}

  4. 4. P(X=1)=0.2P(X=1)=0.2, P(X=2)=0.5P(X=2)=0.5, P(X=3)=0.3P(X=3)=0.3. The median is:

    • A. 11
    • B. 33
    • C. 22
    • D. 2.12.1

  5. 5. Which statement about Var(X)\mathrm{Var}(X) is always true?

    • A. It is greater than E(X)E(X)
    • B. It is equal to E(X2)E(X^2)
    • C. It is less than 11
    • D. It is never negative

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