Tom Peachey has a new post on his blog: The Formula for a Normal Distribution. It is an interesting discussion of how a smarter student may be confused by the pdf of a normal distribution, and in particular by how the pdf and the distribution are affected by a transformation. Please go over to Tom’s blog and give his post a read.
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Students who know how the integral of
, for real constants 
and 
, relates to the integral of 
should have much less of the problems described by Tom.
Thanks, Christian. Have you told Tom?