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Showing posts with the label normal-distribution-standard-deviation

### Parametric Optimal f on the Normal Distribution- FURTHER DERIVATIVES OF THE NORMAL Parametric Optimal f on the Normal Distribution FURTHER DERIVATIVES OF THE NORMAL Sometimes you may want to know the second derivative of the N(Z)  function. Since the N(Z) function gives us the area under the curve at Z,  and the N'(Z) function gives us the height of the curve itself at Z, then  the N"(Z) function gives us the instantaneous slope of the curve at a  given Z: N"(Z) = -Z/2.506628274*EXP(-(Z^2/2) where, EXP() = The exponential function. To determine what the slope of the N'(Z) curve is at +2 standard  units: N"(Z) = -2/2.506628274*EXP(-(+2^2)/2)            = -212.506628274*EXP(-2)            = -2/2.506628274*.1353353            = -.1079968336 Therefore, we can state that the instantaneous rate of change in the  N'(Z) function when Z = +2 is -.1079968336. This represents rise/run,  so we can say that when Z = +2, the N'(Z) curve is rising -.1079968336  for ever) 1 unit run in Z.  Figure  N"(Z) g