Hi Kája, thank you for your comment. I’m glad you liked the post.

For the bus arrival example, the lambda is 4 (arrival in every 15 min = 4 events per hour).

If we plug lambda as 4:**P(T < 10 mins)** **= P(X=0 in 1/6 time units) = 1- e^−(4*0.166) = 1 -e^-0.6667 = 1- 0.5134 = 0.4865**

Here is the relevant part from the post.

**P(T > t)** **= P(X=0 in t time units) = e^−λt*** **T** : **the random variable of our interest!**

the random variable for **the waiting time until the first event**

* **X** : **the # of events in the future which follows the Poisson dist.***** P(T > t) : **The probability that the waiting time until the first event is greater than **t** time units

*** P(X = 0 in t time units) : **The probability of zero successes in **t** time units

For the second question: *2. Ninety percent of the buses arrive within how many minutes of the previous bus?*

You can solve for **t from 1-e^(-4*t)=0.9**