Minimum of Normal Distribution Function

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SUMMARY

The discussion centers on the normal distribution function defined as e^(-(x-μ)^2/(2 σ^2))/(sqrt(2 π) σ). Participants confirm that this function does not have a minimum value. The approach involves taking the derivative of the function and setting it to zero to find critical points, but it is emphasized that further analysis is required to distinguish between maxima and minima. The conclusion is that the normal distribution function approaches zero but never reaches a minimum value.

PREREQUISITES
  • Understanding of calculus, specifically differentiation
  • Familiarity with the properties of the normal distribution
  • Knowledge of critical points and their significance in function analysis
  • Basic grasp of statistical notation and terminology
NEXT STEPS
  • Study the process of finding critical points in functions
  • Learn about the second derivative test for determining maxima and minima
  • Explore the properties of the normal distribution and its applications in statistics
  • Review calculus concepts related to limits and asymptotic behavior
USEFUL FOR

Students studying statistics, mathematicians, and anyone interested in understanding the properties of the normal distribution function and its implications in statistical analysis.

Painguy
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Homework Statement



Show that there is no minimum for the normal distribution function e^(-(x-μ)^2/(2 σ^2))/(sqrt(2 π) σ)

Homework Equations





The Attempt at a Solution



I figured I'd take the derivative and set it equal to 0, but then what?
 
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Painguy said:
I figured I'd take the derivative and set it equal to 0, but then what?
What is the answer you got? And then, how do you tell the difference between a maximum and a minimum?
 

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