options(warn=-1)

Normal Distribution The Normal Distribution is member of parameters mean and variance

it has a probability density function g(x;mean,variance) ==> k exp(1)^{((-1/(2variance))((x-mu)}2))*

the shape of the curve is determined by exp(1)^{((-1/(2variance))((x-mu)}2)) and k is the constant to make this equation probabaility density function.

*k only changes the area under curve not the basic shape

k (constant) is calculated by 1/sqrt(2 pi * sd(x))

so lets create probability density function for normal distribution

norm_dist<-function(x){
  variance = var(x)
  st_dev = sd(x)
  mu = mean(x)
  k = 1 / sqrt(2*pi*st_dev)
  normf <- k * exp(1)^((-1/(2*variance))*((x-mu)^2))
  print(paste("k is : " ,k))
  return(normf)
}

lets create a variable that ranges between -4 and 4

x <- seq(-4, 4, length = 21)

plot probability densities for normal distribution for our vector

plot(x,norm_dist(x),type="b",col="blue",main = paste("Normal Distribution"),ylab="density")

## [1] "k is :  0.25322984419456"

Thanks: Hincal Topcuoglu