Binomial Distributions

PROBABILITY DISTRIBUTIONS

A Probability Distribution is a table of values showing the probabilities of various outcomes of an experiment

CONDITIONS FOR BINOMIAL DISTRIBUTIONS - BERNOULLI process
For understanding, consider example of tossing a coin twice and count the number of times the coin lands on heads.

Fixed number of repeated trials, i.e. n trials

2 coin flips

Independent and Random trials

Outcome is independent of earlier outcomes

Only two outcomes of each trial, either SUCCESS or FAILURE

Either Head or Tail

The probability of success is UNIFORM through out n trials

0.5 Probability of Head as outcome in each flip of a coin

BINOMIAL DISTRIBUTIONS

A binomial random variable is the number of successes x in n repeated trials of a binomial experiment. The probability distribution of a binomial random variable is called a binomial distribution

Suppose we flip a coin two times and count the number of heads (successes). The binomial random variable is the number of heads, which can take on values of 0, 1, or 2. The binomial distribution is presented below

Is a Probability Distribution of Discreet Random Variable
Majorly used for quality control and quality assurance
Also used in service industries like banks to get proportion customers who are satisfied with service quality

NOTE: A discreet variable always contains whole number values. The variable is said to be Random if the sum of the probabilities is one

Using the rules like fixed number of trials(5 times) and probability being same(1/6 for each outcome) for each experiment, we decided to use Binomial Distribution in Example 1.