Question

A random variable X has the PDF $f_X\left(x\right)$ given by
$f_X\left(x\right)=\{\begin{array}{c}Cx{e}^{-x};x>0\\ 0;x\le 0\end{array}$
The the value of C is equal to

• A. 1
• B. 3
• C. 2
• D. 4

Answer 1

The correct option is A 1

${\int }_{\infty }^{\infty }{f}_X\left(x\right)dx=1$
${\int }_0^{\infty }Cx{e}^{-x}dx=1$
$C{[x\left(\frac{e^{-x}}{-1}\right)-1\left(\frac{e^{-x}}{1}\right)]}_0^{-\infty }=1$
$\therefore C(0+1)=1$
$C=1$