<Dl> <Dd> σ = ∫ X (x − μ) 2 p (x) d x, w h e r e μ = ∫ X x p (x) d x, (\ displaystyle \ sigma = (\ sqrt (\ int _ (\ mathbf (X)) (x - \ mu) ^ (2) \, p (x) \, (\ rm (d)) x)), (\ rm (\ \ where \ \)) \ mu = \ int _ (\ mathbf (X)) x \, p (x) \, (\ rm (d)) x,) </Dd> </Dl> <Dd> σ = ∫ X (x − μ) 2 p (x) d x, w h e r e μ = ∫ X x p (x) d x, (\ displaystyle \ sigma = (\ sqrt (\ int _ (\ mathbf (X)) (x - \ mu) ^ (2) \, p (x) \, (\ rm (d)) x)), (\ rm (\ \ where \ \)) \ mu = \ int _ (\ mathbf (X)) x \, p (x) \, (\ rm (d)) x,) </Dd> <P> and where the integrals are definite integrals taken for x ranging over the set of possible values of the random variable X . </P> <P> In the case of a parametric family of distributions, the standard deviation can be expressed in terms of the parameters . For example, in the case of the log - normal distribution with parameters μ and σ, the standard deviation is ((exp (σ) − 1) exp (2μ + σ)). </P>

If the mean is 3 and the standard deviation is 1