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If a continuous random variable X has th...

If a continuous random variable X has the p.d.f. `f(x)=4k(x-1)^(3) 1<=x<=3`, then find `P(1 le X le 2)`.

Text Solution

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The correct Answer is:
`1/16`
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Knowledge Check

  • If a random variable X has the p.d.f. f(x)=k/(x^(2)+1), 0 lt x lt infty , then k is

    A
    `pi`
    B
    `1/pi`
    C
    1
    D
    `2/pi`

  • F(X)=(pi)/(2+tan^(-1))(x)/(pi)-inftyltxltinfty is a distribution of a continous random variable X then P(X le 1) is

    A
    `3/4`
    B
    `1/4`
    C
    `1/2`
    D
    `(pi)/(2)`

  • If F(x)=(A)/(pi)=(1)/(16+x^(2))-inftyltxltinfty is a pdf of a continous random variable x then the value of A is

    A
    16
    B
    8
    C
    4
    D
    1

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    If f(x) = (A)/(pi)(1)/(16+x^(2)),0 ltx lt oo is a probability density function of a continuous random variable X then the value of A is ……… .

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