How can you find standard deviation from a probability distribution?

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Answer 1 · 2018-02-10T19:10:10

$"Standard deviation" = sqrt(E(X^2) - (E(X))^2)$

In a PDF, $f(x)$ , the expected mean is given by $E(X)$

Where $E(X) = int_(-oo) ^(oo) x *f(x) dx$

The variance is given by $Var(x) = E(X^2) - ( E(X) )^2$

Where $E(g(X) ) = int_(-oo) ^(oo) g(x) * f(x) dx$

We know

$"Standard Deviation" = sqrt( "Variance " )$

$=> "Standard deviation" = sqrt(E(X^2) - (E(X))^2)$

Or...

$=> "Standard deviation" =sqrt( int_(-oo) ^(oo) x^2 *f(x) dx -( int_(-oo) ^(oo) x *f(x) dx)^2$