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A binomial experiment is any statistical experiment with the following properties;
Below are Binomial Experiment Examples;
Flipping a coin for a given n number of times is an binomial experiment since there are n trials each with just two outcomes in every trial(head or tail).The probability of head(success) remains the same throughout the experiment(0.5).The outcome of any trial does not influence the outcome in the other.
A random variable is said to follow a binomial distribution if it has n repeated trials and has only two outcomes in each trial. Binomial probability is the probability associated with a binomial experiment in exactly x number of successes. For instance, if a coin is flipped twice and we are interested in the number of tails (successes), we are likely to get either no tail, 1 tail or two tails as shown below;
|No. of tails||Probability|
A binomial distribution has 3 main properties
The mean = n * p
Variance = n * p (1-p)
Standard deviation = √ (n*p (1-p))
Where n is the total number of trials, p is the probability of success and 1-p is the probability of failure.
The Binomial distribution formula is therefore given by;
Basically, real life applications of binomial distribution is anything that you can think of whose outcomes are two: success or failure. Some of the Binomial Experiment Examples are presented below;
Poisson distribution is derived from the binomial probability distribution function. Check here for the entire process
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