Q:
# What is a binomial random variable?

A binomial random variable is a unique type of discrete random variable that counts the frequency of occurrence of a particular event in a fixed number of trials. Several conditions must be met for a variable to be declared a binomial random variable. Two of the conditions are that the number of trials must be fixed and that each trial has only two possible outcomes.

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Other mandatory conditions are that the probability of a success or a failure in each trial must be the same for all the trails, and the outcome of each trial must be independent of the other trials. The binomial random variable has a probability distribution referred to as the binomial distribution.

The mean of the binomial distribution is given by n * P, while its variance is the result of n * P * (1 - P), and the standard deviation is the square root of the variance. The binomial probability, which is the probability of a binomial experiment resulting in X number of successes, can be calculated using the binomial formula, which is written as, b(x; n, P) = {n! / [ X! (n - x)! ]} * P^x * (1 - P)^n - x.

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