Variance
and Standard Deviation
DPD
Find the Variance of a discrete probability distribution (DPD) by multiplying the square of each outcome by its corresponding probability, summing those products, and subtracting the square of the mean.
The formula for the variance of a probability distribution is:
\[\sigma^2=\sum_{i=1}^nP(x_i)\cdot(x_1-\mu)^2\]
There is a quicker (equivalent) formula for variance of a DPD:
\[\Big(\sum_{i=1}^nx_i^2\cdot P(x_i)\Big)-\mu^2\]
The Standard Deviation of a discrete Probability distribution (DPD) is found by taking the square root of the variance.
The formula for the variance of a discrete probability distribution is:
\[\sigma=\sqrt{\sigma^2}=\sqrt{\Big(\sum_{i=1}^n x_i^2\cdot P(x_i)\Big)-\mu^2}\]