Normal Distribution Facts

Probability Level 1

Which of the following is/are true of normal distributions ?

  1. They are always symmetric.
  2. They are never fat-tailed.
  3. They always have a mean of 0.

In this context, fat-tailed would mean having large skewness or kurtosis .

1 only 1 and 2 only 1 and 3 only 2 and 3 only 1, 2, and 3

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Henry Maltby by Henry Maltby , 26, USA

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1 solution

Henry Maltby
Jul 1, 2016

1 and 2 are true.

Normal distributions are defined by their symmetric nature and skinny tails. These elements correpond to null values for skewness and kurtosis. The mean and standard deviation, however, may take on any values (and, in fact, define a normal distribution entirely).

23 Helpful 5 Interesting 3 Brilliant 0 Confused

Wait, but " and stock values were originally estimated in the same way (though they tend to have fatter tails)" ???

Toffiklubitoffi Mrhwa - 3 years, 3 months ago

I’m not sure why #2 would be true. (I’m weak in probability theory.)

J. P. Brooks - 2 years ago

Isn't a log-normal distribution a normal pdf (it is non-symmetric and has large tails) ?

Asif Zaidi - 1 year, 1 month ago

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