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The concept in the probability that summarizes the values taken up by one of the two independent values is known as a binomial distribution.

- Binomial distribution requires set parameters and assumptions for analyses.
- The binomial distribution assumes that there is only one outcome for each trial.
- There are various properties, statistical inferences, and distributions in a binomial distribution.
- The properties of binomial inference are tail bounds, median, mode, expected value and variance, and higher moments.

**Expected value and variance**- When X is a discrete random variable, the expected value of X will be all the possible values that can be taken by X. The occurrence of event weighs the probability of each value. E(X) or m is the way to write expected value. The variance in binomial distribution is denoted by VAR(X). the variance of the sum is the sum of variances of the independent random numbers.**Mode**- In a data set, a mode is a number that occurs the maximum number of times. In binomial distribution, the mode is equal to [(n+1)p] where (n+1)p is a floor number.**Median**- The middle value of the data set, after arranging the data in descending or ascending order is known as the median value. There have been different results and methods to evaluate the median in a binomial distribution.

**Sum of binomial distribution**- The sum of 2 random variables in binomial distribution is also a random variable. For this condition to satisfy, the variables should have the same probability. If the probability is not the same the sum may not be an independent variable**The ratio of binomial distribution**- The ratio of the binomial distribution is approximately distributed with mean log and variance.**Conditional binomials**- In the conditional distribution of Y given by X, Y is a random binomial variable.**Bernoulli distribution-**The distribution of random variable with value 1 probability and value 0 probability in discrete probability is the Bernoulli distribution.**Poisson binomial distribution-**The sum of n independent Bernoulli trials that are non-identical is a special case in binomial distribution known as Poisson binomial distribution.

The other distributions in binomial distribution are a normal approximation, Poisson approximation, limiting distributions, and beta distribution.

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