What is binomial distribution and how does it work?

[sycamorex]

Hi,

Can anyone explain binomial distribution to me. I tried wikipedia and some googling, but I just do not understand much of it. I don't come from
maths background, I am more like an IT person. I need to write a short
program calculating binomial distributions, however, first I need to understand the idea behind it to write the program.

Can you expain it to me in simple terms, or refer to any link providing
a SIMPLE explanation. As I said before, the explanation on wikipidia
doesn't tell me much. Possibly some exercises on it. When do we use it?

Thank you very much in advance
sycamorex

 

[radou]

A keyword which you should find useful while doing some further google-ing: a Bernoulli trial.

Edit: ok ok, I'll google it up from my head in the meantime.

Let there be m independent experiments such that the probability of an outcome A is equal in every of the experiments and is given with P(A) = p. This is a Bernoulli trial. (Example: coin tossing - head or tail.)

Further on, a random variable X = 'the number of times an event A occurred in m experiments in a Bernoulli trial with the probability p' is called a Bernoulli or binomial random variable.

This is a brief explanation.

 

[sycamorex]

thank you
Ok, so if i want to write the computer I would have to have:

probability space - an array of possible outcomes e.g {1,2} tossing a coing, {1,2,3,4,5,6} for rolling a dice.
then I need to state the probability of a particular outcome to happen
e.g P(C)= 0.5 (coins), P(D)=1/6 (dice)

and how can I calculate the binomial distribution of it?

 

[radou]

thank you
Ok, so if i want to write the computer I would have to have:

probability space - an array of possible outcomes e.g {1,2} tossing a coing, {1,2,3,4,5,6} for rolling a dice.
then I need to state the probability of a particular outcome to happen
e.g P(C)= 0.5 (coins), P(D)=1/6 (dice)

and how can I calculate the binomial distribution of it?

You have to apply the probability density function of the binomial distribution, which is given with:
$$f(x) = P(X=k) = \binom{m}{k}p^k (1-p)^{m-k}$$,

where m is the number of experiments and k the number of a specific outcome of the experiment.

 

[sycamorex]

Thanks I think I cracked it:)
so can you confirm it, please
If we take tossing a coin as our experiment
P=0.5
number of trials =4

k=0, probability density function:0.0625
k=1, pdf: 0.25
k=2, pdf: 0.375
k=3, pdf: 0.25
k=4, pdf: 0.0625

is that correct?
thanks

 

[murshid_islam]

yeah you are correct, sycamorex

 

[sycamorex]

thanks, now I will be able to write the program:)