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The Normal Distribution - Introduction to Hypothesis Testing

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In order to understand the fundamentals of hypothesis testing, a basic understanding of the normal distribution is required. A few examples may illustrate the behavior of the normal density function.

Introduction - Function Examples

The following function is investigated:

The Normal Distribution - Introduction to Hypothesis Testing

Obviously, Y > 0 because powers of e are always positive. It is also easy to see that the horizontal axis (X) is a horizontal asymptote for this function:

By the use of this function's first derivative

we conclude that the function:

bulletrises for X < 10 (the derivative is positive)
bulletreaches a maximum at X = 10 (the derivative is zero)
bulletdecreases for X > 10 (the derivative is negative)

The maximum value (at X = 10) is

By the use of the second order derivative

with solutions

we conclude that the function displays two bowpoints :

Voor X=7 of X=13 zijn er dus 2 buigpunten. Beiden hebben als ordinaat

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