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c.d.f. F(x) of a continuous random variable from its p.d.f.

This type of question, asked 4 times: 10 May 2024 S1, 13 May 2024 S2, 19 Apr 2025 S1, 26 Apr 2025 S1. All 4 questions below, oldest first.

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  1. Question 1

    10 May 2024 S1

    104
    p.d.f. f(x)=kx2,  0≤x≤6f(x)=kx^2,\;0\le x\le6. Value of F(4) (c.d.f.) is

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  2. Question 2

    13 May 2024 S2

    128
    The c.d.f. F(x)F(x) associated with p.d.f. f(x)={12x2(1−x),0<x<10,otherwisef(x)=\begin{cases}12x^2(1-x), & 0<x<1\\ 0, & \text{otherwise}\end{cases} is

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  3. Question 3

    19 Apr 2025 S1

    116
    If a random variable X has the p.d.f. f(x)={kx2+1, if 0<x<∞0, otherwise f(x) =\left\{ \begin{matrix} \frac{k}{x^{2}+ 1} & ,\text{~if~}0 <x< \infty \\ 0 & ,\text{~otherwise~} \end{matrix} \right. then c.d.f. of X is

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  4. Question 4

    26 Apr 2025 S1

    134
    The following is p.d.f. of continuous random variable X f(x)={x8, if 0<x<40, otherwise f(x) =\left\{ \begin{matrix} \frac{x}{8} & ,\text{~if~}0 <x< 4 \\ 0 & ,\text{~otherwise~} \end{matrix} \right..Then F(0.5),F(1.7)F(0.5),F(1.7) and F(5)F(5) is respectively

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