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Thread: Continuous random variables

  1. #1
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    Continuous random variables

    Hi,

    I have tried to algebraically manipulate this equation in order to obtain k, however my attempts have been unsuccessful.
    Could someone please help me.

    Thank you and good day sir
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  2. #2
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    Re: Continuous random variables

    Since it's a PDF, the entire area under the graph must equal 1. So

    $\displaystyle \begin{align*} \int_{-\infty}^{\infty}{f\left( y \right) \,\mathrm{d}y} &= 1 \\ \int_{-\infty}^0{0\,\mathrm{d}y} + \int_0^{\infty}{ k\,\mathrm{e}^{-y}\,\mathrm{d}y } &= 1 \\ 0 + \int_0^{\infty}{ k\,\mathrm{e}^{-y}\,\mathrm{d}y } &= 1 \\ k\int_0^{\infty}{\mathrm{e}^{-y}\,\mathrm{d}y} &= 1 \end{align*}$

    Now evaluate the integral and solve for k.
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