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Re: st: standard normal distribution


From   Nick Cox <njcoxstata@gmail.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: standard normal distribution
Date   Mon, 27 Aug 2012 18:21:31 +0100

Yes; this is a radical misunderstanding.

You appear to be averaging densities. Densities can't be negative and so their mean can't be zero. Their SD depends on the sample taken but as the range of density for a standard normal is less than 0.4 (as shown by these results) the SD will be even smaller.

Nick


On 27 Aug 2012, at 16:56, tashi lama <ltashi32@hotmail.com> wrote:

Hello all,
This might be more of a statistical question than stata but I would really appreciate if someone explain me this. I thought I understood normal distribution until I see this. I have a standard normal distribution table with N(mean=0,standard deviation=1) which gives me the following

     x          y
 |---------------|
 | -9   1.03e-18 |
 | -8   5.05e-15 |
 | -7   9.14e-12 |
 | -6   6.08e-09 |
 | -5   1.49e-06 |
 |---------------|
 | -4   .0001339 |
 | -3    .004433 |
 | -2   .0540047 |
 | -1   .2420321 |
 |  0   .3990434 |
 |---------------|
 |  1   .2420321 |
 |  2   .0540047 |
 |  3    .004433 |
 |  4   .0001339 |
 |  5   1.49e-06 |
 |---------------|
 |  6   6.08e-09 |
 |  7   9.14e-12 |
 |  8   5.05e-15 |
 |  9   1.03e-18 |
 | 10   7.70e-23 |
 +---------------+

summ y
Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
          y |        20    .0500127    .1105588   7.70e-23   .3990434

Do I not must get mean of y to be 0 and standard deviation to be 1 since it is a normal distribution N(0,1). Am I misunderstanding something
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