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Math Help - calc2 problem

  1. #1
    jamster114
    Guest

    calc2 problem

    How can I solve this?


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  2. #2
    Global Moderator

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    First,
    p(x)\geq 0.

    Next we need to find,
    \int_{-\infty}^{\infty} p(x)dx
    Subdivide the interval as,
    \int_{-\infty}^0p(x)dx+\int_0^{\infty}p(x)dx
    Since the integral is continous accept at possibly one point we can chose to ignore that fact.
    Now,
    \int_{-\infty}^0 p(x)dx=0 because p(x)=0 for x<0.

    And,
    \int_0^{\infty} p(x)dx=\int_0^{\infty} \lambda e^{-\lambda x}dx

    The anti-derivative is,
    e^{-\lambda x} | ^{\infty}_0 =1
    So it is indeed a probability density function.
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