Computer Science: MFDA

P1: DataFrame

Student_ID <- c()

for(i in 1001:1010) {

+ Student_ID <- append(Student_ID, i)

+ }

Student_ID

Name <- c("jim", "jacy", "ben", "lexi", "john", "suzan", "lee", "emma", "drax", "alice")

Name

Marks <- c(23,34,54,35,65,34,76,45,87,88)

Marks

Gender <- c("male", "female", "male", "female", "male", "female", "male", "female", "male", "female")

Gender

stringAsFactors = FALSE

df <- data.frame(Student_ID, Name, Marks, Gender)

str(df)

summary(df)

extra <- c(1011, "jazz", 44, "male")

df[nrow(df) + 1,] <- extra

data.frame(df$Student_ID, df$Marks)

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P2: Import Export

install.packages("writexl")

library("writexl")

Student_ID <- c()

for(i in 1001:1010) {

+ Student_ID <- append(Student_ID, i)

+ }

Name <- c("jim", "jacy", "ben", "lexi", "john", "suzan", "lee", "emma", "drax", "alice")

Marks <- c(23,34,54,35,65,34,76,45,87,88)

Gender <- c("male", "female", "male", "female", "male", "female", "male", "female", "male", "female")

stringAsFactors = FALSE

df <- data.frame(Student_ID, Name, Marks, Gender)

write.csv(df, file = "D:/University/Sem 4/MFDA/PR/pr2_try1.csv")

write.table(df, file = "D:/University/Sem 4/MFDA/PR/pr2_try2.txt")

df_read1 <- read.csv("D:/University/Sem 4/MFDA/PR/pr2_try1.csv")

df_read2 <- read.table(file = "D:/University/Sem 4/MFDA/PR/pr2_try2.txt")

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P3: Central Tendencies

mean(mtcars$cyl)

mean(mtcars$mpg)

mean(mtcars$gear)

mean(mtcars$disp)

mode<-function(x){which.max(tabulate(x))}

mode(mtcars$cyl)

median(mtcars$cyl)

var(mtcars$cyl)

sd(mtcars$cyl)

boxplot(mpg ~ cyl, data = mtcars, xlab = "Number of Cylinders", ylab = "Miles Per Gallon", main = "Mileage Data")

png(file = "C:/Users/HP/Documents/MFDATrash/line_chart1.jpg")

plot(mtcars$cyl, type = "o", xlab = "Index", ylab = "Cylinders", main = "Cylinders in mtcars DataSet")

dev.off()

png(file = "C:/Users/HP/Documents/MFDATrash/dotplot1.jpg")

dotchart(mtcars$cyl, labels = rownames(mtcars))

dev.off()

hist(mtcars$mpg, xlab = "Miles Per Gallon", ylab = "Number of Cars", main = "Cars Distribution")

hist(mtcars$cyl, xlab = "Cylinders", main = "Histogram for Cylinder in mtcars")

barplot(mtcars$cyl, xlab = "Cars", ylab = "Cylinders", main = "Barplot: Cars and Number of cyl")

barplot (table(mtcars$cyl), main = "Car Distribution", xlab = "Number of Cylinders", col = c("darkblue", "green", "red"), names.arg = c("4 Cylinder", "6 Cylinder", "8 Cylinder"))

pie(table (mtcars$cyl), labels = c("4 Cylinder", "6 Cylinder", "8 Cylinder"), main="Car Distribution")

plot(x = input$cyl, y = input$mpg, xlab = "Number of Cylinders", ylab = "Miles Per Gallon", main = "Scatterplot: Cylinders vs MPG")

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P4: Advanced Visual

sapply(mtcars, function(mtcars) max(mtcars, na.rm = TRUE) - min(mtcars, na.rm = TRUE))

order(mtcars$mpg)

sort(mtcars$mpg)

IQR(mtcars$mpg)

quantile(mtcars$wt, probs = c(0,0.25,0.5,0.75,1))

quantile(mtcars$wt, probs = c(.75, .8))

boxplot(mpg ~ cyl, data = mtcars, xlab = "Number of Cylinders", ylab = "Miles Per Gallon", main = "Mileage Data")

a) 8 cylinders are needed for lowest milage per gallon

b) Prediction with 6 number of cylinders gives maximum confidence

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P5: Prob Dis

x = 0:5

barplot(height = dbinom(x,5,0.4), names.arg = c(0,1,2,3,4,5), xlab = "Number of Late Arrivals", ylab = "Probability", main = "Problem 1")

x = 0:5

barplot(dbinom(x,5,0.1))

barplot(dbinom(x,5,0.3))

When prob is lower, i.e. 0.1: the data is right skewed. When prob increases, the data becomes left skewed. At 0.9, the data is left skewed.ype = "o") / barplot(dpois(x, 3))

x = 1:20

barplot(dbinom(x,20,0.4))

Keeping p = 0.4, and increasing n, the data follows normal distribution.

x <- c(0:4)

dpois(x, 5)

ppois(7, 5, lower.tail = TRUE)

ppois(7, 5, lower.tail = FALSE)

ppois(8,5)-ppois(4,5)

x <- c(1:50)

plot(x, dpois(x, 3), type = "o") / barplot(dpois(x, 3))

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P6: Case Study of Prob Dis

x <- seq(0, 50, by = 1)

y <- dnorm(x, mean = 25.0, sd = 10)

plot(x,y, main = "Normal Distribution", col = "blue")

pnorm(27.5, mean = 22, sd = 29) - pnorm(16.2, mean = 22, sd = 29)

cat("The probability is less than 17: ", pnorm(17, mean = 22, sd = 29))

pnorm(17, mean = 22, sd = 29)

pnorm(15, mean = 22, sd = 29) + (1 - pnorm(25, mean = 22, sd = 29))

pnorm(850000, mean = 1000000, sd = 200000)

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P7: Algebra Op and Dist Met

install.packages("pracma")

a <- c(1,2,3)

b <- c(5,6,7)

dot(a,b)

cross(a,b)

d = matrix(c(1,2,3), nrow=3, ncol=3, byrow=TRUE)

e = matrix(c(4,5,6), nrow=3, ncol=3, byrow=TRUE)

cross(d, e)

f = matrix(c(1,2,3), nrow=1, ncol=3, byrow=TRUE)

t(f)

install.packages("geometry")

install.packages("philentropy")

library(geometry)

library(philentropy)

x <- c(50,5,2)

y <- c(1,8,9)

p <- rbind(x,y)

distance(p, method = "euclidean")

distance(p, method = "manhattan")

distance(p, method = "jaccard")

print('Hamming Distance')

sum(x != y)

d = matrix(c(0.68567, 0.12975, -0.71626, 0.14807, 0.93855, 0.31176, 0.71269, -0.31982, 0.62433), nrow=3, ncol=3, byrow=TRUE)

det(d)

install.packages("matlib")

library(matlib)

e = matrix(c(13, -4, 2, -4, 11, -2, 2, -2, 8), nrow=3, ncol=3, byrow=TRUE)

ev <- eigen(e)

(values <- ev$values)

(vectors <- ev$vectors)

sum(e^2)

sum(values^2)

det(e)

prod(values)

R(e)

sum(values != 0)

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P8: Sampling Dis Techniques

#define number of samples

n = 10000

#create empty vector of length n

sample_means = rep(NA, n)

#fill empty vector with means

for(i in 1:n){

sample_means[i] = mean(rnorm(20, mean=5.3, sd=9))

}

#view first six sample means

head(sample_means) [o/p: [1] 4.304143 6.058354 7.803126 4.667816 4.379790 8.193655]

#create histogram to visualize the sampling distribution

hist(sample_means, main = "", xlab = "Sample Means", col = "steelblue")

#mean of sampling distribution

mean(sample_means)

#standard deviation of sampling distribution

sd(sample_means)

#calculate probability that sample mean is less than or equal to 6

sum(sample_means <= 6) / length(sample_means)

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P9: Estimated Value

install.packages(“MASS”)

library(MASS)

height.survey = survey$Height

mean(height.survey, na.rn = TRUE)

height.response = na.omit(survey$Height)

n = length(height.response)

s = sd(height.response)

SE = s/sqrt(n)

E = qt(.975, df = n-1)*SE

xbar = mean(height.response)

xbar + c(-E, E)

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P10: Hypothesis

xbar = 9900

mu0 = 10000

sigma = 120

n = 30

z = (xbar - mu0) / (sigma/sqrt(n))

alpha = 0.05

z.alpha = qnorm(1-alpha)

-z.alpha (reject)

xbar = 2.1

mu0 = 2

sigma = 0.25

n = 35

z = (xbar - mu0) / (sigma/sqrt(n))

alpha = .05

z.alpha = qnorm(1-alpha)

z.alpha (reject)

Computer Science

Thursday, 30 June 2022

MFDA

P1: DataFrame

P2: Import Export

P3: Central Tendencies

P4: Advanced Visual

P5: Prob Dis

P6: Case Study of Prob Dis

P7: Algebra Op and Dist Met

P8: Sampling Dis Techniques

P9: Estimated Value

P10: Hypothesis

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