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Math Help - continuous random variable

  1. #1
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    continuous random variable

    Please let me know of any errors/wrong logic

    f(x) = { |x| for -1 < x <=1 , 0 elsewhere

    A) Determine Cumulative Distributin Function...

    F(x) = { 0 for x < -1 , -0.5(x^2) for -1 <= x < 0 , 0.5(x^2) for 0 <= x <= 1, 1 for x >1

    B) F(-0.25)

    (-0.5)(-0.25)^2 = -0.03125

    I thought that it should yield a positive value...

    C) Pr(-0.25 <= X <= 0.5)

    F(B) - F(A) = F(0.5) - F(-0.25) = (0.5)(0.5)^2 - (-0.5)(-0.25)^2 = 0.4375
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  2. #2
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    Quote Originally Posted by DINOCALC09 View Post
    Please let me know of any errors/wrong logic

    f(x) = { |x| for -1 < x <=1 , 0 elsewhere

    A) Determine Cumulative Distributin Function...

    F(x) = { 0 for x < -1 , -0.5(x^2) for -1 <= x < 0 , 0.5(x^2) for 0 <= x <= 1, 1 for x >1 Mr F says: There are multiple obvious errors with this answer. According to this:

    1. F(0) = 0 ....? Surely F(0) = 0.5.

    2. F(x) < 0 for -1 \leq x < 0 which is obviously wrong.

    3. F(1) = 0.5 and so your cdf is not continuous.

    B) F(-0.25)

    (-0.5)(-0.25)^2 = -0.03125

    I thought that it should yield a positive value...

    C) Pr(-0.25 <= X <= 0.5)

    F(B) - F(A) = F(0.5) - F(-0.25) = (0.5)(0.5)^2 - (-0.5)(-0.25)^2 = 0.4375
    You need to fix up your answer to part (a) before worrying about the other parts. I hope you know that |x| = -x for x < 0 and so for x < 0, F(x) = \int_{-1}^x (-u) \, du ....
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  3. #3
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    Ok so I think I figured it out:

    F(x) =

    0 for x< -1
    (1-x^2)/2 for -1 <= x <= 0
    (1+x^2)/2 for 0 < x <= 1
    1 for x > 1

    Now how would I go about finding the IQR here?

    Thanks
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  4. #4
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    Quote Originally Posted by DINOCALC09 View Post
    Ok so I think I figured it out:

    F(x) =

    0 for x< -1
    (1-x^2)/2 for -1 <= x <= 0
    (1+x^2)/2 for 0 < x <= 1
    1 for x > 1

    Now how would I go about finding the IQR here?

    Thanks
    Get the 25th and 75th percentiles and then take the difference of them.
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