# Exponential Distribution Expected Value

Question 1 (part 1)

I was attempting to use the exponential distribution to solve the following problem:

the time between cars passing on a road can be modelled with an avg rate of 3.5 cars per minute. Find the probability that the time between two comsecutive cars passing the road is between 20 and 40 seconds

I have set lamda to be 0.0583/sec.

Question 1 (part 2)

While what I am going to ask has nothing to do with solving my question, it leaves me curious (since i am really sincere about learning stats):

If I did E(x) = 1/lamda = 17.15

May i say that this value is the average cars passing per sec? But it doesnt seem to make sense here

Answer to Question 1 (part 1)

The answer to the original question is:

Find P (20 < x < 40)

Lamda = 0.0583 per sec

P(x<40) = 1 - e ^ -(0.0583)(40) = 0.9029

P(x<20) = 1 - e ^ -(0.0583)(40) = 0.6884

Therefore P (20 < x < 40) = 0.9029 - 0.6884 = 0.2145

If theres a better way to do this, I will be glad to learn.

What is wrong with the answer you've given? Seems fine to me. Also that $17.15$ is the average waiting time between cars. So this means you expect one car every $17.15$ seconds. Note that this is consistent with $3.5$ cars per minute as $17.15\times 3.5=60$ seconds.