Binomial Distribution
The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials. It is used to model situations where there are only two possible outcomes for each trial, such as success or failure.
Parameter of Binomial Distribution
The binomial distribution has two parameters, n and p, where n is the number of trials and p is the probability of success on any given trial.
Given, x is a binomial variate with parameter 15 and 1/3
Mode of Binomial Distribution
The mode of a distribution is the value that occurs most frequently in the distribution.
For a binomial distribution, the mode can be calculated as follows:
Mode = [np], if np is an integer
Mode can be either [np] or [np]+1, if np is not an integer
where [ ] represents the greatest integer function.
Calculating Mode of Binomial Distribution
Using the above formula, we can calculate the mode of the given binomial distribution as follows:
np = 15 x 1/3 = 5
Since np is an integer, the mode of the distribution is:
Mode = [np] = [5] = 5
