Assignmen3

Q1.

Create an R function to calculate factorials. You are not allowed to use the built-in function factorial().

1.function name is

"new"

## [1] "new"

2.Argument is n 3.If function distinglish n>1 or n<1 1When n < 1, return 1. 2When n > 1, return factorials.

new <- function(n){
  j <- 1                #j set up 1
  save<-NULL 
  while(j <= length(n)){  #j set up number of n 
    if(n[j] == 0){        #When n[j] is zero  
      save<-c(save,1)     #save 1. In other words ,n = 1.  
    }else{A <- 1          #A set up 1 
    while(n[j] >= 1){     #When n>1,factorial(from 1 to n)
      A <- n[j]*A         #A reset up 1*n[j]
      n[j] <- n[j]-1}     #n[j] is number of n-1
    save<-c(save,A)}      
    j <- j+1              #j plus 1, and again(until number of n)
  }  
  return(save)            #output n! 
}

Q2

Using your own factorial function, create an R function to calculate the number of possible combinations that can be obtained by taking a subset of elements from a larger set. 1.function name is

 'kf'

## [1] "kf"

kf <- function(n,k) # using former function. Substitute former n,K for function
{return(new(n)/(new(k)*new(n-k)))
}

Q3

Using your own combination function, create an R function to calculate the probability mass of binomial distributions. You are not allowed to use the built-in function dbinom().

pf <- function(n,x,p) # using former function.
{return(kf(n,x)*p^x*(1-p)^(n-x)) 
}

Q4

Using your own binomial PMF, display graphically the PMF of binomial dis-ributions for n = 2; 5; 10; and 50.

1.P is 0.5 and 0.3.

2. Using Q3’s function.

P is 0.5.

 #n is 2 and x is 0:2
x <- 0:2
plot(x, pf(2,x,.5))

 #n is 5 and x is 0:5
x <- 0:5
plot(x, pf(5,x,.5))

 #n is 10 and x is 0:10
x <- 0:10
plot(x,pf(10,x,.5))

 #n is 50 and x is 0:50
x <- 0:50
plot(x,pf(50,x,.5))

p is 0.3

 #n is 2 and x is 0:2
x <- 0:2
plot(x, pf(2,x,.3))

 #n is 5 and x is 0:5
x <- 0:5
plot(x, pf(5,x,.3))

 #n is 10 and x is 0:10
x <- 0:10
plot(x,pf(10,x,.3))

 #n is 50 and x is 0:50
x <- 0:50
plot(x,pf(50,x,.3))

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