Exponential distribution law algorithm?

Question

Mathematics

At the university, they were asked to write a program for modeling events.
I write in php.
The task is not difficult, but I can not understand this part of the condition: The
interval (delta)t obeys an exponential law with a mathematical expectation equal to 10 seconds.
I can not understand / imagine the scheme of actions for calculating these intervals.
How to calculate this interval?
PS: complete condition of the problem:
On the communication line, which consists of 2 channels, at random intervals of time t, information packages are received. When a message arrives, each of the channels can be busy with a probability of 0.4. If both channels are busy. That information is lost. The interval t obeys an exponential law with a mathematical expectation equal to 10 seconds.
Determine what percentage of packages are lost within an hour.

Answer 1

Formula for a random number with exponential distribution:
R _i = -1 * ln(W _i ) / λ, where λ is the intensity, and W _i is a random number from 0 to 1.
Mat. expectation in this case is the reciprocal of intensity.
If I understand correctly, then in your case the formula will look like
deltaT = -M * ln(W _i )

Answer 2

Are you familiar with statistics?
Do you know what a Gaussian distribution is? Have you read
here ?

Answer 3

It is not clear why the statistics of packet arrival and the time of the experiment are needed at all. It is enough that “the communication line consists of 2 channels… When a message arrives, each of the channels can be busy with a probability of 0.4. If both channels are busy, then the information is lost. It is clear that no matter how the parcels arrive, an average of 16% will be lost.