Poisson distribution algorithm for product orders?

Question

PHP

Hello.
In a test task, I encountered a requirement to implement the receipt of orders using the Poisson distribution.
Unfortunately, I haven’t come across this before, I just can’t figure out how to apply this distribution? I found the MathPHP
library There is such a function:

// Poisson distribution
$λ       = 2; // average number of successful events per interval
$k       = 3; // events in the interval
$poisson = new Discrete\Poisson($λ);
$pmf     = $poisson->pmf($k);
$cdf     = $poisson->cdf($k);

The task itself:

Orders arrive randomly with an interval of 1-30 minutes and have a
Poisson distribution. An order has the following properties:
1. order number;
2. arrival time (starts from 0);
3. cooking time (10-30 min);
....
Generate N orders according to properties. (N=10...100);

Answer 1

Unfortunately, this is a task, not a question. especially test.
by the way, all this is googled, and even especially you don’t need to delve into applied statistics. although it is a shame not to know what the distribution of a random variable is