# what do we mean by $\mathcal{N}(0,1)$?

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

• Both. It refers to the distribution which is characterised by either the cdf. or the pdf. – copper.hat Feb 14 at 7:04
• Is it wrong to say "$\mathcal{N}(0,1) =_d$ >>insert pdf/cdf of standard normal distribution<<" ? – LocalMartingale Feb 14 at 7:11
• 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. – copper.hat Feb 14 at 7:16
• How about if i write "=". ? – LocalMartingale Feb 14 at 7:17
• 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 $\Phi$. – copper.hat Feb 14 at 7:34