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Math Help - finding the CDF

  1. #1
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    finding the CDF

    Please refer to the attached image.

    For part a)

    when I want to find the CDF, don't I simply take the indefinite integral of e^-|x|, multiply it by c and solve for that = 1?

    I am unsure of how to take the integral for this, am i correct in saying it is -e^-x, for all x ?

    that would leave me with c* -e^-x = 1, and c = 1/(-e^-x), wolfram says there are two separate results, but i am not sure why. and in that case, I would also have two separate results for c. how can that make sense?

    for part b) i am unsure as to how to approach the question. could someone please guide me?

    As always, your help is very much appreciated and invaluable.

    Thanks
    Attached Thumbnails Attached Thumbnails finding the CDF-assignment2-question.png  
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  2. #2
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    Re: finding the CDF

    When integrating absolute values you must split up the integration into two parts, the first part where the expression inside the absolute value is always non negative and the second part where the expression inside the absolute value is always non positive.

    For example g(x)= |x+2| Find \int_{-10}^5g(x)dx

    \int_{-10}^5|x+2|dx=\int_{-10}^{-2}|x+2|dx+\int_{-2}^5|x+2|dx

    \int_{-10}^{-2}|x+2|dx+\int_{-2}^5|x+2|dx=\int_{-10}^{-2}-(x+2)dx+\int_{-2}^5(x+2)dx
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