Please read [[wp>Normal_distribution|Normal Distribution]] at Wikipedia.org first.

__좌우대칭__이며 __asymtotic__한 분포를 이루는 것을 정상분포라고 한다. 수학적으로 정상분포는 아래와 같이 정의된다.
\begin{equation} 
\displaystyle P(x) = \frac{1}{\sqrt{2 \pi \sigma^2}} * e^{\frac{-(x - \mu)^2}{2 \sigma^2}} 
\end{equation}  
위에서 $\pi$와  $e$ 는 각각 $\pi = 3.1416, e=2.7183 $으로 상수

특히 평균이 0 이고 그 표준편차가 1인 정상분포를 표준정상분포라고 한다. 

{{http://math.arizona.edu/~rsims/ma464/standardnormaltable.pdf|표준정규분포 table}}
https://www.mathsisfun.com/data/standard-normal-distribution-table.html

<code>set.seed(3000)
xseq<-seq(-4,4,.01)
densities<-dnorm(xseq, 0,1)
cumulative<-pnorm(xseq, 0, 1)
randomdeviates<-rnorm(1000,0,1)
 
par(mfrow=c(2,2), mar=c(3,4,4,2))

plot(xseq, densities, col="darkgreen",
   xlab="", ylab="Density", type="l", lwd=2, cex=2, 
   main="PDF of Standard Normal", cex.axis=.8)

plot(xseq, cumulative, col="darkorange", 
   xlab="", ylab="Cumulative Probability",type="l",lwd=2, cex=2, 
   main="CDF of Standard Normal", cex.axis=.8)

hist(randomdeviates, main="Random draws from Std Normal", 
   cex.axis=.8, xlim=c(-4,4))

xseq<-seq(-4,4,.01)
y<-2*xseq + rnorm(length(xseq),0,5.5)
hist(y, prob=TRUE, ylim=c(0,.06), breaks=20)
curve(dnorm(x, mean(y), sd(y)), add=TRUE, col="darkblue", lwd=2)

par(mfrow=c(1,1))
</code>
{{:pasted:20240313-082705.png}}