Madonna
and child, painted by Sandro
Botticelli

3
keywords in this discussion are random variables, the sample space
and probability. Random variable is a function that goes from a
sample space to a measurable space.

Sample
space is part of a probability space. A sample space is a set of all
the possible "outcomes" that may arise in an experiment.

Now,
we make example to understand the concept. Let’s say that we have a
coin. The coin has Head=H and Tail=T.

Then,
we flipped the coin 4 times. The possible outcomes are: 2 and trials
are 4.

We
determine Sample Space = S = 2^4 = 16 = { HHHH, HTHH, THHH, HTHT,
HHHT, HTTH, TTHH, THTH, HHTT, HHTH, TTTH, THHT, HTTT, TTTT, TTHT,
THTT}

_{}

^{}

Virgin,
child and angels, painted by Sandro
Botticelli

Let’s
say we just interest on the number of heads in four flips:

x
= number of heads in four flips of a coin.

The
random variable x could equal 0, 1, 2, 3, or 4.

We
can determine the probability of x values by computing:

x=
0 = p(0)= probability no head = 1/16 = 0.0625

x
= 1 = p(1)= probability 1 head = 4/16 = 0.25

x
= 2 = p (2)= probability 2 heads = 6/16 = 0.375

x
= 3 = p (3)= probability 3 heads = 4/16 = 0.25

x
= 4 = p (4)= probability 4 heads = 1/16= 0.0625

By
following this concept, we can determine the probability of tails
too.