Mean and variance of continuous random variables

Mean and variance of continuous random variables Quiz

Spec 2.3 · Edexcel A-Level Further Maths: Quiz

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  1. 1. A continuous random variable has f(x)=x8f(x)=\frac{x}{8} on 0≤x≤40\le x\le4. Find E(X)\mathrm{E}(X).

    • A. 83\frac{8}{3}
    • B. 22
    • C. 163\frac{16}{3}
    • D. 43\frac{4}{3}

  2. 2. If E(X)=4\mathrm{E}(X)=4 and E(X2)=19\mathrm{E}(X^2)=19, what is Var(X)\mathrm{Var}(X)?

    • A. 1515
    • B. 2323
    • C. 33
    • D. 3\sqrt{3}

  3. 3. The median mm of a distribution with cumulative distribution function FF satisfies

    • A. F(m)=0F(m)=0
    • B. F(m)=1F(m)=1
    • C. f(m)=0.5f(m)=0.5
    • D. F(m)=0.5F(m)=0.5

  4. 4. A distribution has mean 1212, median 1010 and mode 77. Describe its skewness.

    • A. Negative skew
    • B. Positive skew
    • C. Zero skew
    • D. Cannot be determined

  5. 5. With F(x)=1−x−3F(x)=1-x^{-3} for x≥1x\ge1, the 75th percentile solves

    • A. 1−x−3=0.751-x^{-3}=0.75
    • B. x−3=0.75x^{-3}=0.75
    • C. 1−x−3=0.251-x^{-3}=0.25
    • D. 3x−4=0.753x^{-4}=0.75

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