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
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.