What is binomial distribution and how does it work?

In summary, the conversation discusses binomial distribution and its application in writing a computer program. The concept of a Bernoulli trial, probability density function, and calculating the binomial distribution are explained in simple terms. The conversation also mentions the need for a probability space and how to determine the probability of a specific outcome. The final part confirms the correct calculations and the ability to write the program.
  • #1
sycamorex
4
0
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
 
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  • #2
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. :smile:

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.
 
Last edited:
  • #3
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?
 
  • #4
sycamorex said:
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:
[tex]f(x) = P(X=k) = \binom{m}{k}p^k (1-p)^{m-k}[/tex],

where m is the number of experiments and k the number of a specific outcome of the experiment.
 
  • #5
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
 
  • #6
yeah you are correct, sycamorex
 
  • #7
thanks, now I will be able to write the program:)
 

1. What is a binomial distribution?

A binomial distribution is a probability distribution that describes the likelihood of a certain number of successes in a fixed number of independent trials, where each trial has two possible outcomes (success or failure) and the probability of success remains constant.

2. How is a binomial distribution different from other probability distributions?

A binomial distribution is unique because it only considers two possible outcomes (success or failure) and a fixed number of trials. Other probability distributions, such as the normal distribution, can have an infinite number of outcomes and trials.

3. What is the formula for calculating the probability of a specific number of successes in a binomial distribution?

The formula for calculating the probability of exactly x successes in n trials, with a probability of success p, is P(x) = (nCx)(p^x)(1-p)^(n-x), where nCx is the binomial coefficient.

4. How is the binomial distribution used in real-life scenarios?

The binomial distribution is commonly used in statistics to model the probability of success in repeated independent trials, such as in gambling or quality control processes. It can also be used in fields like biology, medicine, and psychology to analyze data from experiments with dichotomous outcomes.

5. What is the relationship between the binomial distribution and the central limit theorem?

The central limit theorem states that the sum of a large number of independent and identically distributed random variables will be approximately normally distributed, regardless of the underlying distribution. The binomial distribution is one of the distributions that can approximate a normal distribution when the number of trials is large. This relationship allows us to use the normal distribution to make inferences and calculations about binomial data, making it a useful tool in statistical analysis.

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