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Name Class Roll No Instructor Assignment: Muhammad Zeeshan Nazar CS-8 (B) 160612 Sir Saad 2

This document contains a student's assignment submission containing 7 exercises involving the use of random number generation and probability distribution functions in R. The assignment includes generating random numbers from uniform and multinomial distributions, plotting density plots, calculating binomial and Poisson probabilities, and summing binomial probabilities.

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Muhammad Zeeshan Nazar Nazar Din
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47 views6 pages

Name Class Roll No Instructor Assignment: Muhammad Zeeshan Nazar CS-8 (B) 160612 Sir Saad 2

This document contains a student's assignment submission containing 7 exercises involving the use of random number generation and probability distribution functions in R. The assignment includes generating random numbers from uniform and multinomial distributions, plotting density plots, calculating binomial and Poisson probabilities, and summing binomial probabilities.

Uploaded by

Muhammad Zeeshan Nazar Nazar Din
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Name Muhammad Zeeshan Nazar

Class CS-8(B)
Roll No 160612
Instructor Sir Saad
Assignment 2
Exercise 1 
set.seed​(1) 
random_numbers <- ​runif​(100, min = .5, max = 6.5) 
(​round​(random_numbers)) 

## [1] 2 3 4 6 2 6 6 4 4 1 2 2 5 3 5 3 5 6 3 5 6 2 4 1 2 3 1 3 6 3 3 4 3 2 5 5 5 
## [38] 1 5 3 5 4 5 4 4 5 1 3 5 5 3 6 3 2 1 1 2 4 4 3 6 2 3 2 4 2 3 5 1 6 3 6 3 3 
## [75] 3 6 6 3 5 6 3 5 3 2 5 2 5 1 2 1 2 1 4 6 5 5 3 3 5 4 

Exercise 2 
set.seed​(1) 
(dice_result <- ​rmultinom​(n=30, size = 1, prob = ​rep​(1​/6
​ ,6))) #
​ rolling dice 

## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14] 
## [1,] 0 0 1 0 0 0 0 0 0 0 0 0 0 0 
## [2,] 0 1 0 0 0 0 0 0 0 0 0 0 0 0 
## [3,] 0 0 0 0 1 1 1 0 1 0 1 0 0 0 
## [4,] 1 0 0 0 0 0 0 0 0 0 0 1 0 1 
## [5,] 0 0 0 0 0 0 0 0 0 0 0 0 1 0 
## [6,] 0 0 0 1 0 0 0 1 0 1 0 0 0 0 
## [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26] 
## [1,] 0 0 0 0 0 0 0 1 0 0 0 0 
## [2,] 1 0 0 0 0 1 0 0 0 0 0 0 
## [3,] 0 0 0 0 0 0 0 0 1 0 0 0 
## [4,] 0 0 1 0 1 0 1 0 0 0 0 1 
## [5,] 0 0 0 0 0 0 0 0 0 1 0 0 
## [6,] 0 1 0 1 0 0 0 0 0 0 1 0 
## [,27] [,28] [,29] [,30] 
## [1,] 0 0 0 0 
## [2,] 0 0 0 1 
## [3,] 0 0 0 0 
## [4,] 0 0 0 0 
## [5,] 1 1 1 0 
## [6,] 0 0 0 0 

sum​(dice_result[6,]​==​1) #
​ checking total 6's 

## [1] 6 
Exercise 3 
apply​(dice_result, 1, f​ unction​(x){ 
​sum​(x​==​1) 
}) 

## [1] 2 4 6 7 5 6 

Exercise 4 
set.seed​(1) 
heights <- r​ norm​(n = 700, mean = 1.70, sd = .1) 
plot​(d
​ ensity​(heights), main = 'Simulating Heights') 
 
 
set.seed​(1) 
heights2 <- ​rnorm​(n = 10000, mean = 1.70, sd = .1) 
lines​(d​ ensity​(heights2), col = 'red', lwd = 2) 

Exercise 5 

Part A 
x <- ​seq​(0,50,by = 1) 
y <- ​dbinom​(x,50,0.5) 
plot​(x,y) 
 
a <- ​seq​(0,50,by = 1) 
b <- ​pbinom​(x,50,0.5) 
plot​(a,b) 
 

Exercise 6 
ppois​(12, lambda = 15) ​#lower tail 

## [1] 0.267611 

ppois​(12, lambda = 15, lower = FALSE) #


​ upper tail 

## [1] 0.732389 

Exercise 7 
#lambda <- rgamma(n = 1,shape = 20, scale = .5) 
#set.seed(1) 
#rpois(n = 1, lambda = lambda) 
#---------------------------------------- 
a <- ​dbinom​(14, size = 22, prob = 0.7) 
print​(a) 

## [1] 0.1422919 

b <- ​pbinom​(13, size = 22, prob = 0.7) 


print​(b) 

## [1] 0.1864574 
c <- ​sum​(d
​ binom​(11​:​22, size = 22, prob = 0.7)) 
print​(c) 

## [1] 0.9859649 

#or 
d <- 1​-pbinom​(10, size = 22, prob = 0.7) 
print​(d) 

## [1] 0.9859649 

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