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This question already has an answer here:

I have a basic question about the probability density function of the standard normal distribution $X\sim N(0,1)$. I understand that the cumulative distribution function for x is $P(X\le x)$ (in R language it can be obtained by pnorm(x,mean =0, sd =1)). However, I don't understand what $f(x)$ represents (in R: dnorm(x,mean =0, sd =1)) ? $$ f(x) = \frac{1} { \sqrt{2\pi } } e^{ -x^2/ 2} $$

Note that for a discrete random variable, like the binomial distribution, it is equivalent to $P(Y=x)$.

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marked as duplicate by Tim Oct 20 '18 at 6:34

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  • $\begingroup$ You can find the explanation from internet or textbook. For example, onlinecourses.science.psu.edu/stat414/node/97 $\endgroup$ – user158565 Oct 20 '18 at 6:00
  • $\begingroup$ Thanks for the link. According to the definition, f(x) does not represent anything, only it is helpful in finding getting P(X<x). $\endgroup$ – Aryo Z Oct 20 '18 at 8:16
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Firstly the density is dnorm not pnorm

The density is simply the derivative (rate of change) of the distribution function “pnorm” at the value specified

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