Probability distributions using R Experiment :1 Binomial Distribution Experiment :2 Poisson Distribution Experiment :3 Normal Distribution

 #Lab-8

#Program 1 Probability distribution

b1=pbinom(4,12,0.2)  #n=12 p=0.2

b2=dbinom(3,12,0.2)

b3=sum(dbinom(2:4,12,0.2))

b4=rbinom(3,12,0.2)

b5=1-pbinom(3,12,0.2)

b6=1-pbinom(5,12,0.2)

b7=sum(dbinom(0:6,12,0.2))

b1

b2

b3

b4

b5

b6

b7

#Program 2

#n=6 #p=0.5

b1=dbinom(2,6,0.5)

b2=1-pbinom(4,6,0.5)

b3=1-pbinom(0,6,0.5)

b1

b2

b3

#Poisson Distribution

#Program 1

n=2000

p=0.001

dpois(3,lambda=n*p)

ppois(2,lambda=n*p,lower=FALSE)

#Program 2

ppois(17,lambda = 12) #Left Tailed

#Other Program

ppois(17,lambda = 12,lower=FALSE) #Right Tailed

#Program 3

ppois(2,lambda = 4) #Left Tailed

dpois(3,lambda=4)

#Normal Distribution

#dnorm Ex-1

dnorm(0,mean=0,sd=1)

#Ex-2

z_scores=seq(-3,3,by=0.1)

dvalues=dnorm(z_scores)

dvalues

#pnorm EX-1

pnorm(0)

#EX-2

pnorm(2,mean = 5,sd=3,lower.tail = F)

#EX-3

1-pnorm(2,mean = 5,sd=3,lower.tail = FALSE)

#qnorm

#EX-1

qnorm(0.5)

#EX-2

qnorm(0.96)

#Pnorm

#Program-1

mu=485

sigma=0.1*mu

pnorm(400,mu,sigma)

#Program 2

y=pnorm(26,mean=30,sd=5)

x=pnorm(40,mean = 30,sd=5)

x-y

#Program 3

x=pnorm(60,mean=34.5,sd=16.5)

y=pnorm(30,mean = 34.5,sd=16.5)

x-y

cat("number of students expected to obtain marks between 30 and 60",1000*(x-y))

#Program 4

qnorm(.98,mean=100,sd=20)

#STUDENT PRACTICE

#Binomial Distribution

b1=pbinom(6,10,0.4)

b1

b2=dbinom(6,10,0.4)

b2

b3=sum(dbinom(3:6,10,0.4))

b3

b4=rbinom(6,10,0.4)

b4

b5=1-b1

b5

#Poisson Distribution

n=1000

p=0.01

dpois(4,lambda=n*p)

ppois(4,lambda = n*p)

ppois(4,lambda = n*p,lower.tail=F)

#Normal Distribution

x=pnorm(45,mean=30,sd=5)

y=1-x

y

dnorm(3,mean=6,sd=2)

pnorm(3,mean=6,sd=2)

qnorm(0.66)

y=pnorm(35,mean=10,sd=4)

x=pnorm(69,mean = 20,sd=3)

x-y