Mathematical formula with Rplot

How to plot Mathematical formula with R

x <- seq(0,10,0.1)

> x

  [1]  0.0  0.1  0.2  0.3  0.4  0.5  0.6

  [8]  0.7  0.8  0.9  1.0  1.1  1.2  1.3

 [15]  1.4  1.5  1.6  1.7  1.8  1.9  2.0

 [22]  2.1  2.2  2.3  2.4  2.5  2.6  2.7

 [29]  2.8  2.9  3.0  3.1  3.2  3.3  3.4

 [36]  3.5  3.6  3.7  3.8  3.9  4.0  4.1

 [43]  4.2  4.3  4.4  4.5  4.6  4.7  4.8

 [50]  4.9  5.0  5.1  5.2  5.3  5.4  5.5

 [57]  5.6  5.7  5.8  5.9  6.0  6.1  6.2

 [64]  6.3  6.4  6.5  6.6  6.7  6.8  6.9

 [71]  7.0  7.1  7.2  7.3  7.4  7.5  7.6

 [78]  7.7  7.8  7.9  8.0  8.1  8.2  8.3

 [85]  8.4  8.5  8.6  8.7  8.8  8.9  9.0

 [92]  9.1  9.2  9.3  9.4  9.5  9.6  9.7

 [99]  9.8  9.9 10.0

> windows(7,4)

> par(mfrow=c(1,2))

> y <- exp(x)

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

> y <- log(x)

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

> windows(7,7)

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

> x <- seq(0,2*pi,2*pi/100)

> y1 <- cos(x)

> y2 <- sin(x)

> y3 <- tan(x)

> plot(y1~x,type="l",main="cosine")

> plot(y2~x,type="l",main="sine")

> plot(y3~x,type="l",ylim=c(-3,3),main="tangent")

> x <- seq(0,1,0.01)

> y <- xˆ0.5

Error: unexpected input in "y <- xˆ"

> y <- x^0.5

> plot(x,y,type="l",main="0<b<1")

> y <- x

> plot(x,y,type="l",main="b=1")

> y <- x^2

> plot(x,y,type="l",main="b>1")

> y <- 1/x

> plot(x,y,type="l",main="b<0")

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

> y1 <- 2+5*x-0.2*x^2

> y2 <- 2+5*x-0.4*x^2

> y3 <- 2+4*x-0.6*x^2+0.04*x^3

> y4 <- 2+4*x+2*x^2-0.6*x^3+0.04*x^4

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

> plot(x,y1,type="l",ylab="y",main="decelerating")

> plot(x,y2,type="l",ylab="y",main="humped")

> plot(x,y3,type="l",ylab="y",main="inflection")

> plot(x,y4,type="l",ylab="y",main="local maximum")

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

> y1 <- x/(2+5*x)

> y2 <- 1/(x-2+4/x)

> y3 <- 1/(xˆ2-2+4/x)

Error: unexpected input in "y3 <- 1/(xˆ"

> y3 <- 1/(x^2-2+4/x)

> plot(x,y1,type="l",ylab="y",main="Michaelis-Menten")

> plot(x,y2,type="l",ylab="y",main="shallow hump")

> plot(x,y3,type="l",ylab="y",main="steep hump")

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

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

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

> abline(h=1,lty=2)

> e0 <- 10

> n0 <- 10

plot

> plot(e0,n0,ylab="",xlab="",ylim=c(0,2*n0),xlim=c(0,2*e0),type="n")

> n <- 1000

> r <- 10

> for (i in 1:n) {

+     a <- point(r)

+     e <- e0+a[1]

+     n <- n0+a[2]

+     lines(c(e0,e),c(n0,n),col= "red")

+ }

Error in point(r) : could not find function "point"

> for (i in 1:n) {

+     a <- points(r)

+     e <- e0+a[1]

+     n <- n0+a[2]

+     lines(c(e0,e),c(n0,n),col= "red")

+ }

 par(mfrow=c(2,2))

> 

> hist(sample(1:6,replace=T,10000),breaks=0.5:6.5,main="",xlab="one die")

> a <- sample(1:6,replace=T,10000)

> b <- sample(1:6,replace=T,10000)

> hist(a+b,breaks=1.5:12.5,main="", xlab="two dice")

> c <- sample(1:6,replace=T,10000)

> hist(a+b+c,breaks=2.5:18.5,main="", xlab="three dice")

> d <- sample(1:6,replace=T,10000)

> e <- sample(1:6,replace=T,10000)

> hist(a+b+c+d+e,breaks=4.5:30.5,main="", xlab="five dice")

> mean(a+b+c+d+e)

[1] 17.4211

> sd(a+b+c+d+e)

[1] 3.819428

> lines(seq(1,30,0.1),dnorm(seq(1,30,0.1),17.5937,3.837668)*10000)

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

> curve(dnorm,-3,3,xlab="z",ylab="Probability density",main="Density")

> curve(pnorm,-3,3,xlab="z",ylab="Probability",main="Probability")

> curve(qnorm,0,1,xlab="p",ylab="Quantile (z)",main="Quantiles")

> y <- rnorm(1000)

> 

> hist(y,xlab="z",ylab="frequency",main="Random numbers") 

> yvals <- rnorm(100,24,4)

> mean(yvals)

[1] 24.20079

> sd(yvals)

[1] 4.485446

> ydevs <- rnorm(100,0,1)

> ydevs <- (ydevs-mean(ydevs))/sd(ydevs)

> mean(ydevs)

[1] 1.832519e-17

> sd(ydevs)

[1] 1

> yvals <- 24 + ydevs*4

> mean(yvals)

[1] 24

> sd(yvals)

[1] 4

 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")

> 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)

> 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

 python