Linear combinations of Normal random variables

Linear combinations of Normal random variables Quiz

Spec 4.1 · Edexcel A-Level Further Maths: Quiz

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  1. 1. X∼N(10,22)X\sim N(10,2^2) and Y∼N(7,32)Y\sim N(7,3^2) are independent. What is the distribution of X+YX+Y?

    • A. N(17, 13)N(17,\ 13)
    • B. N(17, 25)N(17,\ 25)
    • C. N(3, 5)N(3,\ 5)
    • D. N(17, 5)N(17,\ 5)

  2. 2. With XX and YY as above, what is the variance of X−YX-Y?

    • A. 55
    • B. −5-5
    • C. 11
    • D. 1313

  3. 3. X∼N(5,4)X\sim N(5,4). What is the variance of 3X3X?

    • A. 1212
    • B. 3636
    • C. 44
    • D. 66

  4. 4. X1X_1 and X2X_2 are independent, each N(20,32)N(20,3^2). What is the distribution of X1+X2X_1+X_2?

    • A. N(40, 36)N(40,\ 36)
    • B. N(40, 9)N(40,\ 9)
    • C. N(40, 18)N(40,\ 18)
    • D. N(20, 18)N(20,\ 18)

  5. 5. To find P(A>B)\mathrm{P}(A>B) for independent Normal AA and BB, you find

    • A. P(A+B>0)\mathrm{P}(A+B>0)
    • B. P(A−B>0)\mathrm{P}(A-B>0)
    • C. P(AB>1)\mathrm{P}(AB>1)
    • D. P(A>B)\mathrm{P}(A>B) directly

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