Distributions

Binomial Mean and Variance

For a binomial random variable with n trials and success probability p:

μ = np
σ² = np(1-p)

Example

Use np for the mean and npq for the variance.

highlighted = computed this step

Step 1 — Parameters

List n, p, and q.

n=10p=12q=12n= \hl{10} \quad p= \hlmath{\frac{1}{2}} \quad q= \hlmath{\frac{1}{2}}

Step 2 — Mean

Use n times p for the mean.

μ=10⋅12=5\mu= 10 \cdot \frac{1}{2} = \hl{5}

Step 3 — Variance

Use n times p times q for variance.

σ2=10⋅12⋅12=52\sigma^{2}= 10 \cdot \frac{1}{2} \cdot \frac{1}{2} = \hlmath{\frac{5}{2}}

Step 4 — Standard deviation

Take the square root for standard deviation.

σ=52\sigma=\sqrt{ \hlmath{\frac{5}{2}} }
binomial-mean-variance μ = np and σ² = np(1-p)