Probabilities in R: The normal distribution

R has functions to compute values of probability density functions (p.d.f.) and cumulative distribution functions (c.m.d.) for most common distributions.

Explanation

par(mfrow=c(2,1))
t<-seq(-5,5,0.01)
plot(t,dnorm(t),type="l")

x<-seq(-5,5,0.01)
plot(x,pnorm(x),type="l")

Top: The probability density function for the normal distribution. Bottom: The cumulative distribution function for the normal distribution.

For example the normal density:
$$p(t)=\frac{1}{\sqrt{2\pi}}e^{-\frac{t^2}{2}}$$

Details

The p.d.f. for the normal distribution is

$$p(t)=\frac{1}{\sqrt{2\pi}}e^{-\frac{t^2}{2}}$$

The c.d.f. for the normal distribution is

$$\Phi(x)=\int\limits_{-\infty}^x\frac{1}{\sqrt{2\pi}}e^{-\frac{t^2}{2}}dt$$

Examples

\begin{xmpl}
dnorm() gives the value of the normal p.d.f.
\end{xmpl}
\begin{xmpl}
pnorm() gives the value of the normal c.d.f.
\end{xmpl}