# Thread: Cumulative and distribution functions.

1. ## Cumulative and distribution functions.

I honestly don't know how to start this problem and any help would be appreciated.

"In 1950 an experiment was done observing the time gaps between successive cars on the Arroyo Seco Freeway. The data show that the density function of these time gaps was given approximately by p(x)=ae^(-0.122x) where x is the time in seconds and a is a constant.

a) Find a."

That's not the whole question, but this is the one I'm confused about. How am I to find a, with little information?

2. Originally Posted by Rumor
I honestly don't know how to start this problem and any help would be appreciated.

"In 1950 an experiment was done observing the time gaps between successive cars on the Arroyo Seco Freeway. The data show that the density function of these time gaps was given approximately by p(x)=ae^(-0.122x) where x is the time in seconds and a is a constant.

a) Find a."

That's not the whole question, but this is the one I'm confused about. How am I to find a, with little information?
It's been a while, but here's a stab at it ...

I believe that the constant "a" can be found if one remembers that the area under a pdf = 1. Since x represents time between consecutive cars, then the limits of integration would be $0$ to $\infty$ , no?

I get $a = 0.122$