# Relationship between Poisson and exponential distribution

Studying the probability of waiting time between two orders where the number of calls in a given period of time follows a Poisson distribution, a seller got the following probability density function for the waiting time:

$$f(W) = 0.2e^{(−0.2W)}$$

where the waiting time $$W$$ is measured in minutes. In this case, obtain the probability of getting at least two calls in $$5$$ minutes.

I wonder what are the relationships between the exponential distribution and Poisson distribution in this example. I mean, what should the parameter lambda of the Poisson distribution be?

I thought, because the given time interval is $$5$$ (minutes) and the parameter of the exponential distribution above is $$0.2$$, the lambda should be $$5*0.2=1$$?

Is this correct?

Hence, if you find the holding/waiting times between some random events are i.i.d. and distributed exponentially with parameter $$\lambda$$, then the total number of events will be distributed as a Poisson distribution with parameter $$\lambda t$$.