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Homework Help: Roots of the normal distribution

  1. Nov 11, 2014 #1
    1. The problem statement, all variables and given/known data
    $$f:\mathbb{R} \rightarrow \mathbb{R},$$

    $$ f(x) = \frac{1}{\sigma \sqrt{2 \pi}} e^{\frac{-(x-\mu)^2}{2 \sigma ^{2}}}$$

    What are the roots of this equation?

    2. Relevant equations

    3. The attempt at a solution

    The roots of an equation are the values of [itex]x[/itex] such that [itex]f(x) = 0[/itex]. This is the first time I have seen a question like this and am still getting my head around the normal distribution, but as far as i'm aware the curve never does reach [itex]f(x) = 0[/itex] so I want to express the idea that the roots of this equation are [itex]+/- \infty[/itex] but I don't know how to do this...

    [itex]lim_{x \rightarrow +/- \infty} f(x) = 0[/itex]

    I'd appreciate some guidance,

    thanks :)
  2. jcsd
  3. Nov 11, 2014 #2


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    Gold Member

    It doesn't look to me like you need much guidance on this. You have it exactly correct. But I wouldn't say the roots are ##\pm \infty##. Just say it has no roots but the limit is 0 as you have stated.
  4. Nov 11, 2014 #3
    Well that is good news, thanks!
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