Question

let x be a random variable with probability density function given by f(x)=(2he^-1/4x ; 0<x find the value of constant h

Answer 1

$$\displaystyle\int_{-\infin}^{\infin}f(x)dx=1$$

$$\displaystyle\int_{0}^{\infin}2he^{-x/4}fdx=\lim\limits_{t\to\infin}\int_{0}^{A}2he^{-x/4}fdx$$

$$=\lim\limits_{t\to\infin}[-8he^{-x/4}]\begin{matrix} t\\ 0 \end{matrix}=8h=1$$

$$h=1/8$$