If X is a continuous random variable having distribution function F , then its median is defined as that value

If X is a continuous random variable having distribution function F , then its
median is defined as that value of m for which
F (m) = 1/2
Find the median of the random variable with density function
(a) f (x) = e^(−x) , x ≥ 0

f(x) = e^(−x)

F(x) = ∫[0,x] f(u) du
= ∫[0,x] e^(-u) du
= -e^(-x) - (-e^0)
= 1 - e^(-x)

1 - e^(-x) = 1/2
e^(-x) = 1/2
e^x = 2
x = ln(2)

The median is ln(2).