Question

The probability density function of a random variable X is given by, If ''a'' and "b'' are two positive real constants, then the correct relation between the constants a and b will be

$f_x\left(x\right)=a{e}^{-b|x|}$

• A. b = 2a
• B. ab = 1
• C. a = 2b
• D. a = b

Answer 1

The correct option is A b = 2a



From the basic properties of probability density function

${\int }_{-\infty }^{\infty }$f(x) dx = 1

$f_x\left(x\right)$ is am even function

So, $2{\int }_0^{\infty }a{e}^{-bx}dx=1$

$2a\left[\frac{e^{-bx}}{-b}\right]{|}_0^{\infty }=1$

$\frac{2a}{b}=1$

b = 2a