The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution function f(x) = 0, x< 0, 1 − e −8x, x≥ 0. find the probability of waiting less than 12 minutes between successive speeders (a) using the cumulative distribution function of x; (b) using the probability density function of x.
so we're looking for [tex]\mathbb P\left(X<\dfrac15\right)[/tex].
The CDF gives us this value right away, since [tex]F_X(x)=\mathbb P(X<x)=\mathbb P(X\le x)[/tex] for any continuous random variable [tex]X[/tex] with distribution function [tex]F_X(x)[/tex]: