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Math Help - continuous distribution

  1. #1
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    continuous distribution

    X is a random variable with probability density function defined as:

    f(x) = {
    2sin(4x), a <= x <= b
    0, elsewhere
    }

    find a and b?
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  2. #2
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    You know that the value your function must be non-negative.
    The total area under the curve must be 1.
    Therefore, let a=0 and find b.
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  3. #3
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    hmm, if i let a=0, i get the wrong answer straight away.

    The book says: PI/2, 3*PI/4 for a and b respectively.

    I tried solving the question and i got 0 <= x <= PI/4 -- which seems to be also correct, as the answer they give is basically exactly 1 period later.
    Since 0 + PI/2 = PI/2, and PI/4 + PI/2 = 3*PI/4

    So i think i basically got it right, just that my answer wasnt any of the multiple choices.

    Btw, the way i solved it (which is basically what you said) was:

    2sin(4x) >= 0
    sin(4x) >= 0
    4x >= asin(0)
    4x >= 0, PI
    x >= 0, PI/4

    so 0 <= x <= PI/4

    and i checked the integral from 0 - PI/4 of 2sin4x to make sure it == 1.
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