Distributions  Some Questions
Probability distributions describe the possible outcomes of experiments.
They are in some kind a universal description of the underlying random
processes. In order to give a first impression, consider the questions
below. The answers to the questions could be found easily if we knew the
probability distributions of the involved processes.

We flip a coin fifty times. How often will the head
be up?

We flip a coin again and again: When will the head
be up the first time?

We flip 20 coins at once for thirty times. Tell me
more about the number of heads expected to be seen.

Delta Motors Inc. produced 100,000 cars. 20,000 cars
from this series are already sold to cardrivers, 80,000 cars are still
at car dealers. Now technicians detect a mistake in construction. According
to their calculation, 3% of the cars of this series will cause troubles
during usage. The supervisory board of the company wants to know the probability
of more than 1,000 cars showing this defect.

A physicist baked a cake, mixing exactly 75 raisins
into the dough. The cake is then cut into 8 equal pieces. Picking one piece,
he counts 15 raisins in this piece of cake. Being very astonished about
this fact (he expected 9 or 10 raisins), he wants to know the probability
of finding 15 raisins in this piece.

The FBSPD (Federal Bureau of Statistics and Population
Dynamics) is interested in the distribution of the bodyheight of the population
(adults).

Epsilon Insurance Inc. needs to calculate the risk
of a client dying before his 60th birthday.

What is the intensity of light in the center and
at the border of a groundglass screen?
