Variance for the Binomial distribution is similarly calculated using the n and p parameters. Let's use the 10 fair coin flips example to try to understand how variance is calculated. Each coin flip has a certain probability of landing as heads or tails: 0.5 and 0.5, respectively.
The variance of a single coin flip will be the probability that the success happens times the probability that it does not happen: p(1-p), or 0.5 x 0.5. Because we have n = 10 number of coin flips, the variance of a single fair coin flip is multiplied by the number of flips. Thus we get the equation:
Let's consider our 20 multiple choice quiz again. The variance around getting an individual question correct would be p(1-p), or 0.25 x 0.75. We then multiply this variance for all 20 questions in the quiz and get:
$$
Variance(NumberOfCorrectAnswers) = 20 x 0.25 x (1-0.25) = 3.75
$$
We would expect to get 5 correct answers, but the overall variance of the probability distribution is 3.75.
Variance for the Binomial distribution is similarly calculated using the n and p parameters. Let's use the 10 fair coin flips example to try to understand how variance is calculated. Each coin flip has a certain probability of landing as heads or tails: 0.5 and 0.5, respectively.
The variance of a single coin flip will be the probability that the success happens times the probability that it does not happen: p(1-p), or 0.5 x 0.5. Because we have n = 10 number of coin flips, the variance of a single fair coin flip is multiplied by the number of flips. Thus we get the equation:
$$ Variance(NumberOfHeads) = Var(X) = n.p.x(1-p) $$
$$ Variance(NumberOfHeads) = 10x0.5x(1-0.5) = 2.5 $$
Let's consider our 20 multiple choice quiz again. The variance around getting an individual question correct would be p(1-p), or 0.25 x 0.75. We then multiply this variance for all 20 questions in the quiz and get:
$$ Variance(NumberOfCorrectAnswers) = 20 x 0.25 x (1-0.25) = 3.75 $$
We would expect to get 5 correct answers, but the overall variance of the probability distribution is 3.75.