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Math Help - probability density

  1. #1
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    probability density

    Please give me some guidlance on the following problem :


    Let
    X be a random variable such that its values lie in the interval [1 1] and consider the function

    f
    : [1 1]- R f (x) = ((x\2) +1 ) * e^(x-1) .

    a) Prove that
    f can be the probability density of X.

    b) Compute the expected value of
    X.


    Many thanks,

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  2. #2
    MHF Contributor matheagle's Avatar
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    PLease explain......

    f
    : [1 1]- R f (x) = ((x\2) +1 ) * e^(x-1) .

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  3. #3
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    Let X be a random variable such that its values lie in the interval [1 1] and consider the function

    f: [-1,1] in the set of real numbers and we have
    f(x) = ((x\2) +1 ) * e^(x-1)

    a) Prove that f can be the probability density of X.
    b) Compute the expected value of
    X.

    Hope now it's clear for you Unfortunately it's not for me . Please give me some guidance.

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  4. #4
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    Quote Originally Posted by saskadimova View Post
    Let X be a random variable such that its values lie in the interval [1 1] and consider the function


    f: [-1,1] in the set of real numbers and we have
    f(x) = ((x\2) +1 ) * e^(x-1)

    a) Prove that f can be the probability density of X.
    b) Compute the expected value of X.

    Hope now it's clear for you Unfortunately it's not for me . Please give me some guidance.

    a) You need to show that \int_{-1}^{1} \left( \frac{x}{2} + 1\right) e^{x-1} \, dx = 1.

    b) You need to calculate \int_{-1}^{1} x \left( \frac{x}{2} + 1\right) e^{x-1} \, dx.

    In both cases integration by parts is a way of doing this.
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