How can you find standard deviation from a probability distribution?
Risposta:
# "Standard deviation" = sqrt(E(X^2) - (E(X))^2) #
Spiegazione:
In a PDF, #f(x) # , the expected mean is given by #E(X) #
Dove #E(X) = int_(-oo) ^(oo) x *f(x) dx #
The variance is given by #Var(x) = E(X^2) - ( E(X) )^2 #
Dove #E(g(X) ) = int_(-oo) ^(oo) g(x) * f(x) dx #
Sappiamo che
# "Standard Deviation" = sqrt( "Variance " ) #
#=> "Standard deviation" = sqrt(E(X^2) - (E(X))^2) #
O...
#=> "Standard deviation" =sqrt( int_(-oo) ^(oo) x^2 *f(x) dx -( int_(-oo) ^(oo) x *f(x) dx)^2 #