Question

Q: Help in understanding and solving this example from Data Structure & Algorithms (Computer Science) with the steps of the solution to better understand, thanks.

**Using R studio language, thanks.

R Lab:

You need to use R commands and using R markdown to generate a report that interacted with statistics R. A sample program is provided.

x =0:20

 theta<-3

 pdff<- (1/theta)*exp(-x/theta)
 cdff<- 1-exp(-x/theta) 
 
 plot(x, pdff, type ='l')

Instructions:

1. Use R command to generate a sample of random numbers from the exponential distribution , with theta =5

a. You need to generate n =100*k, k is 8.

b. Generate the histogram of the random numbers generated, and overlaying it with the p.d.f of the exponential distribution.

So, the inverse of the exponential c.d.f is y=−θln(1−x), for 0≤x≤1

Based on the theorem in section 5.1 in the textbook, the algorithm for generating n varieties from an Exponential (θ

) distribution is:

1. Generate u1,...,un

n<-50
 theta<-3
 u<-runif(n,0,1)
 y<-(-theta)*log(1-u)
 
 x.range <- range(y)
breaks <- seq(min(x.range),max(x.range),length=20)

# Produce hist of the non drug measurements, then drug measurements on top
hist(y, breaks=breaks, probability=TRUE, xlim=x.range, col="red")
lines(breaks, dexp(breaks, rate = 1/3))

2.Your R markdown program should generate a report that shows the simulation process. Please send the report and your raw code.

a.In the report, you should draw the p.d.f. and c.d.f. of the exponential distribution.

b.You should add in your own conclusion on what you have observed in the histogram,

comparing it to the p.d.f. overlaying on it.

Answer 1

#Code Explained in comments:

QUESTION:1

#MUltiplication of x and y means :Adding x and x 'y' times

x <- 6 # Assign 6 value to x
y <- 7 #Assign 7 to y

cnt <-0 #Assign counter =0 for counting the loop purpose
sum <-0 #Intialise sum=0
while(cnt < y) #while counter<y it will add sum +x and stores in sum ,increment the counter and by the end of the loop,sum contains product of X AND y
{

sum=sum+x
cnt=cnt+1

}

print("Multiplication of x and y by addition concept:")#Displays on console
print(sum) #Displays the product of x and y as sum vaiable on console

//OUTPUT:

QUESTION:2(Divison by subtraction)

#Division of x and y means :Subtracting y from x untill x>=y

#suppose if we want to caluclate division of 43 by 7 ....If we subtract 7 from 43 --6 times the remainder will be 1 and quotient is how much times we subtracted y from x until x>=y i.e 6times

x <- 42 # Assign 42 value to x
y <- 7 #Assign 7 to y
print("x value :")
print(x)
print ("y value:")

print(y)

quotient <-0 #Intialise quotient=0 and used for couning purpose about how much times we subtracted y from x for every iteration
while(x>=y) #As discussed at the start of this answer described we will run the loop satisfying condition x>=y
{

x=x-y
quotient=quotient+1 #increment the quotient counter by 1 for every loop
}

print("Division of x and y by subtraction concept:")#Displays on console

print("QUOTIENT:")

print(quotient) #Displays the quotient vaiable on console

print("remainder:")

print(x) #displays remainder as current value of x

//OUTPUT: