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Math Help - continuous random variables

  1. #1
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    continuous random variables

    A continuous random variable Y has pdf (probability density function)
    f
    (y) = 2eky , y > 0
    1/ 6, − 6 < y < −3


    (a)
    Determine the value of the constant k. Then sketch the pdf.
    Finally, derive and sketch
    Y's cdf (cumulative distribution function).

    (b)
    Find Y's mean, variance and standard deviation.


    (c)
    Find Y's mode and median.


    Hi there,

    I have done part of the question and want to cross check the answers i got.

    a) k= -4

    cdf

    F(y) = 0 y<-6
    (1/6)y -6<y<-3
    { [(1/6) (3- 3e^(-4y) +y]} y>0


    b) E(Y) = (169/16) + [ (-y/4)e^ (-4y) - ((1/16)e^(-4y))

    Please, correct me if I am wrong

    Cheers
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  2. #2
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    Quote Originally Posted by chris2009 View Post
    A continuous random variable Y has pdf (probability density function)


    f
    (y) = 2eky , y > 0
    1/ 6, − 6 < y < −3


    (a)


    Determine the value of the constant k. Then sketch the pdf.
    Finally, derive and sketch Y's cdf (cumulative distribution function).

    (b)


    Find Y's mean, variance and standard deviation.

    (c) Find Y's mode and median.

    Hi there,

    I have done part of the question and want to cross check the answers i got.

    a) k= -4

    cdf

    F(y) = 0 y<-6
    (1/6)y -6<y<-3
    { [(1/6) (3- 3e^(-4y) +y]} y>0


    b) E(Y) = (169/16) + [ (-y/4)e^ (-4y) - ((1/16)e^(-4y))

    Please, correct me if I am wrong

    Cheers

    Your value of k looks OK.

    E(Y) should not depend on y ..... Calculate a value. Preferably show your working to make the checking easier.

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