Binomial distribution variance

To find the variance of a discrete random variable in a binomial distribution, we multiply the expectation of the binomial DRV by the probability of failure (one minus the probability of success).

We can write that as:

\text{for }X\sim B(n,p) \quad Var(X)=E(X)\times (1-p)

As we know that E(X)=np, we can write:

\text{for }X\sim B(n,p) \quad Var(X)=n\,p\,(1-p)

flashcards

QuestionAnswer
What is the formula for variance in a binomial distribution?\text{For } X \sim B(n,p),\quad Var(X)=n\,p\,(1-p)
How is the variance of a binomial distribution expressed in terms of expectation?Var(X) = E(X) \times (1-p)
What does 1-p represent in binomial variance?The probability of failure.
What is E(X) for a binomial distribution X \sim B(n,p)?E(X)=np