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 #