Given that the random variable X has the following cumulative distribution function F(x) = 1 - e^-x, for x > 0. Find the probability density function, f(x), for the random varaible X. f(x) = -e, for x> 0 f(x) = e^-x, for X > 0 f(x)=e^-x for -infinity Solution taking derivative of F(x), we get: f(x) = e^(-x) for x>0 (option (B)).

1. Given that the random variable X has the following cumulative distribution function F(x) = 1 -
e^-x, for x > 0. Find the probability density function, f(x), for the random varaible X. f(x) = -e,
for x> 0 f(x) = e^-x, for X > 0 f(x)=e^-x for -infinity
Solution
taking derivative of F(x), we get: f(x) = e^(-x) for x>0
(option (B))