when we say $\mathcal{N}(0,1)$ for instance, do we refer to the p.d.f or the c.d.f?

  • $\begingroup$ Both. It refers to the distribution which is characterised by either the cdf. or the pdf. $\endgroup$ – copper.hat Feb 14 at 7:04
  • $\begingroup$ Is it wrong to say "$\mathcal{N}(0,1) =_d$ >>insert pdf/cdf of standard normal distribution<<" ? $\endgroup$ – LocalMartingale Feb 14 at 7:11
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    $\begingroup$ When you write $=_d$ it means two random variables are equal in distribution. ${\cal N}(0,1)$ refers to a distribution not a random variable. $\endgroup$ – copper.hat Feb 14 at 7:16
  • $\begingroup$ How about if i write "=". ? $\endgroup$ – LocalMartingale Feb 14 at 7:17
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    $\begingroup$ Not really. As I said above, it refers to the distribution, not the cdf. If I write $X \sim {\cal N}(0,1)$ it means that $X$ has a standard normal distribution and the cdf. of $X$ is $\Phi$. $\endgroup$ – copper.hat Feb 14 at 7:34

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