"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow. The pdf of X is the following.
f(x) = 0.15e−0.15(x − 0.5) x ≥ 0.5
0 otherwise

What is the probability that time headway is more than 6 sec? At least 6 sec?

Question

"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow. The pdf of X is the following.
f(x) = 0.15e−0.15(x − 0.5)	    	x ≥ 0.5
              0		otherwise

What is the probability that time headway is more than 6 sec? At least 6 sec?