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Is binomial probability independent?
The underlying assumptions of the binomial distribution are that there is only one outcome for each trial, that each trial has the same probability of success, and that each trial is mutually exclusive, or independent of each other.
Can you add binomials?
Adding binomials together requires the combining of like terms. The only way to get a binomial for an answer when adding is if the first and second terms of both binomials are like terms. You multiply binomials by using the distributive property across the parentheses.
Is the sum of two binomial distributions?
In probability theory and statistics, the sum of independent binomial random variables is itself a binomial random variable if all the component variables share the same success probability. If success probabilities differ, the probability distribution of the sum is not binomial.
When is the sum of independent variables A binomial variable?
In probability theory and statistics, the sum of independent binomial random variables is itself a binomial random variable if all the component variables share the same success probability. If success probabilities differ, the probability distribution of the sum is not binomial.
How to calculate the sum of two binomial distributions?
If you let X = X A + X B be the random variable which is the sum of your two binomials, then P ( X = k) is the summation over all the ways that you get X A = k A and X B = k B where k A + k B = k. It is easy to write down this summation formula if you know the formulas for binomial distribution, and summation notation.
What is the binomial sum variance inequality in statistics?
See the binomial sum variance inequality. Here is an excerpt from the Wikipedia page. In probability theory and statistics, the sum of independent binomial random variables is itself a binomial random variable if all the component variables share the same success probability.
Is the sum of X and Y independent?
It is evident that X and Y are independent. Now realize that X + Y = B1 + ⋯ + Bn + m is binomially distributed with parameters n + m, p. This spares you any computations. Just compute. Suppose X ∼ Bin(n, p), Y ∼ Bin(m, p).