Normal Distribution

 How do you read normal distribution?

The normal distribution is a continuous probability distribution. The normal distribution is used to study the behavior of continuous random variables like weight, height, and intelligence of a group of students.

How to plot normal distribution in data science?

z <- seq(-3,3,0.01)

> pd <- dnorm(z)

> plot(z,pd,type="l")

> p<-seq(9800,10500,50)

> pda<-dnorm(p)

> plot(p,pda,type="l")

> polygon(c(z[z<=-1],-1),c(pd[z<=-1],pd[z==-3]),col="red")

curve(x^3-3*x, -2, 2)

> x <- seq(-2,2,0.01)

> y <- xˆ3-3*x

Error: unexpected input in "y <- xˆ"

> y <- x^3-3*x

> plot(x,y,type="l")

> x <- seq(-2,2,0.01)

> y <- x^3-3*x

> plot(x,y,type="l")

> xv <- 0:100

> yA <- 482*xv*exp(-0.045*xv)

> yB <- 518*xv*exp(-0.055*xv)

> plot(c(xv,xv),c(yA,yB),xlab="stock",ylab="recruits",type="n")

> lines(xv,yA,lty=2,col="blue")

> lines(xv,yB,lty=1,col="red")

> points(x,y,pch=16)

 values <- rpois(1000,1.70)

> hist(values,main="",xlab="random numbers from a Poisson with mean 1.7")

> hist(values,breaks=(-0.5:8.5),main="",

+      xlab="random numbers from a Poisson with mean 1.7")

> y <- rnbinom(158,mu=1.5,size=1)

> bks <- -0.5:(max(y)+0.5)

> hist(y,bks,main="")

> mean(y)

[1] 1.367089

> var(y)

[1] 3.2784

> mean(y)ˆ2/(var(y)-mean(y))

Error: unexpected input in "mean(y)ˆ"

> mean(y)^2/(var(y)-mean(y))

[1] 0.9778265

> xs <- 0:11

> ys <- dnbinom(xs,size=1.2788,mu=1.772)

> lines(xs,ys*158)

> par(mfrow=c(1,1))

> t <- seq(0.2,4,0.01)

> plot(t,gamma(t),type="l")

> abline(h=1,lty=2)

> par(mfrow=c(2,2))

> x <- seq(0,10,0.1)

> y <- 100/(1+90*exp(-1*x))

> plot(x,y,type="l",main="three-parameter logistic")

> y <- 20+100/(1+exp(0.8*(3-x)))

> plot(x,y,ylim=c(0,140),type="l",main="four-parameter logistic")

> x <- -200:100

> y <- 100*exp(-exp(0.02*x))

> plot(x,y,type="l",main="negative Gompertz")

> x <- 0:100

> y <- 50*exp(-5*exp(-0.08*x))

> 

> plot(x,y,type="l",main="positive Gompertz")

> a <- 10

> b <- -0.8

> c <- 10

> d <- -0.05

> y <- a*exp(b*x)+c*exp(d*x)

> plot(x,y,main="+ - + -",type="l")

> a <- 10

> b <- -0.8

> c <- 10

> d <- 0.05

> y <- a*exp(b*x)+c*exp(d*x)

> plot(x,y,main="+ - + +",type="l")

> par(mfrow=c(1,1))

> x <- 0:6

> plot(x,factorial(x),type="s",main="factorial x",log="y")

> choose(8,3)

[1] 56

> plot(0:8,choose(8,0:8),type="s",main="binomial coefficients")

> curve(pnorm(x),-3,3)

> arrows(-1,0,-1,pnorm(-1),col="red")

> arrows(-1,pnorm(-1),-3,pnorm(-1),col="green")

> pnorm(-1)

[1] 0.1586553

> curve(dnorm(x),-3,3)

> par(mfrow=c(2,2))

> x <- seq(-3,3,0.01)

> x <- seq(-3,3,0.01)

> plot(x,y,type="l",main= "x")

Error in xy.coords(x, y, xlabel, ylabel, log) : 

  'x' and 'y' lengths differ

> y <- exp(-abs(x))

> plot(x,y,type="l",main= "x")

> y <- exp(-abs(x)^2)

> plot(x,y,type="l",main= "x^2")

> y <- exp(-abs(x)^3)

> plot(x,y,type="l",main= "x^3")

> y <- exp(-abs(x)^8)

> plot(x,y,type="l",main= "x^8")

> pnorm(-1.25)

[1] 0.1056498

> pnorm(1.875)

[1] 0.9696036

> 1-pnorm(1.875)

[1] 0.03039636

> pnorm(1.25)-pnorm(-0.625)

[1] 0.6283647

> z <- seq(-0.635,1.25,0.01)

> p <- dnorm(z)

> z <- c(z,1.25,-0.635)

> p <- c(p,0,0)

> plot(x,dnorm(x),type="l",xaxt="n",ylab="probability density",xlab="height")

> axis(1,at=-3:3,labels=c("146","154","162","170","178","186","192"))

> polygon(z,p,col="red")