Expected Value and Variance of a Binomial Random Variable

4. Probability Distributions: Common Distributions

Expected Value and Variance of a Binomial Random Variable

Expected Value of a Binomial Random Variable

To calculate the expected value of a binomial random variable $X\sim B(n,p)$ , use the following formula:

$\mathbb{E}[X] = n\cdot p$

Suppose $X$ has a binomial distribution with parameters $n=25$ and $p=0.2$ .

Calculate the expected value of $X$ .

$\mathbb{E}[X]=5.0$

To calculate the expected value of a binomial random variable $X\sim B(n,p)$ , use the following formula:
$\mathbb{E}[X]=n \cdot p=25 \cdot 0.2 = 5.0$

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Variance and Standard Deviation of a Binomial Random Variable

To calculate the variance of a binomial random variable $X\sim B(n,p)$ , use the following formula:

$\sigma^2 = n\cdot p \cdot (1-p)$
To calculate the standard deviation, take the positive square root of the variance:

$\sigma = \sqrt{\sigma^2} = \sqrt{n\cdot p \cdot (1-p)}$

Suppose $X$ has a binomial distribution with parameters $n=25$ and $p=0.2$ .

Calculate the variance of $X$ . Round your answer to $2$ decimal places.

$\sigma^2=4.00$

To calculate the variance of a binomial random variable $X\sim B(n,p)$ , use the following formula:

$\sigma^2 = n\cdot p \cdot (1-p) = 25 \cdot 0.2 \cdot (1-0.2) = 4.00$

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