Part-discrete part-continuous distributions

Part-discrete part-continuous distributions Quiz

Spec SD1 · AQA A-Level Further Maths: Quiz

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  1. 1. P(X=0)=0.5P(X=0)=0.5 and f(x)=kxf(x)=kx for 0<x≤10<x\le1. Find kk.

    • A. 0.50.5
    • B. 22
    • C. 11
    • D. 0.250.25

  2. 2. P(X=0)=0.3P(X=0)=0.3 and f(x)=0.35f(x)=0.35 for 0<x≤20<x\le2. Find P(X≤1)P(X\le1).

    • A. 0.350.35
    • B. 0.650.65
    • C. 0.70.7
    • D. 11

  3. 3. Which statement is true for a part discrete, part continuous XX with P(X=0)=0.4P(X=0)=0.4?

    • A. P(X=1)>0P(X=1)>0
    • B. P(X≤0)=0P(X\le0)=0
    • C. P(X=0)=0.4P(X=0)=0.4 and P(X=1)=0P(X=1)=0
    • D. ∫f(x) dx=1\int f(x)\,dx=1

  4. 4. P(X=0)=0.6P(X=0)=0.6 and the rest is continuous. What is the median of XX?

    • A. 0.60.6
    • B. 0.50.5
    • C. 11
    • D. 00

  5. 5. P(X=0)=0.2P(X=0)=0.2 and f(x)=0.4xf(x)=0.4x for 0<x≤20<x\le2. Find P(X>1)P(X>1).

    • A. 0.40.4
    • B. 0.60.6
    • C. 0.80.8
    • D. 0.30.3

Quiz