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Thread: Probability distributions

  1. #1
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    Probability distributions

    Please help. The question is : Let the distribution function of X for x>0 be Probability distributions-image-035.jpg
    What is the density function of X for x>0?
    The answer is Probability distributions-image-036.jpg.


    some of the steps areProbability distributions-image-039.jpg

    Probability distributions-image-040.jpg
    Probability distributions-image-042.jpg
    Probability distributions-image-043.jpg
    Please can anyone show me step by step. I really don't understand. Thank you very much.
    Attached Thumbnails Attached Thumbnails Probability distributions-image-033.jpg   Probability distributions-image-038.jpg   Probability distributions-image-041.jpg  
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  2. #2
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    Re: Probability distributions

    Hey imp120.

    Have you tried differentiating each term in the series? Can you please show us your work?
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    Re: Probability distributions

    Probability distributions-image-044.jpg



    Thank you very much.. I am a self learning , didn't go to school. Don't know what to do on this question.
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    Re: Probability distributions

    Probability distributions-image-046.jpg

    Thank you so much for helping
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  5. #5
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    Re: Probability distributions

    Quote Originally Posted by imp120 View Post
    Click image for larger version. 

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    Since you are 'self-studding' it appears that your weakness is really in calculus.
    That will make much of this impossible for you to follow.
    $D_x(x^ke^{-x})=kx^{k-1}e^{-x}-x^ke^{-x}$ the $\large-$ comes from the derivative of $e^{-x}$.
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