//week-1//
my_function <- function() {
  print("Hello World!")
}
my_function()

new_function <- function(fname){
  paste(fname, "Herondale")

}

new_function("will")
new_function("james")
new_function("jace")

ab <- function(f,l){
  paste(f,l)
}
ab("c", "C")

cd <- function(country="Swedan"){
  paste("I am from", country)
}
cd()
cd("India")

//week-2//

#binomial
x <- seq(0,50,by = 1)
y <- dbinom(x,50,0.5)
png(file = "dbinom.png")
plot(x,y)
dev.off()

pbinom(3, size = 13, prob = 1 / 4)
plot(0:10, pbinom(0:10, size = 10, prob = 1 / 4), type = "l")

#geometric distributionn
x_dgeom <- seq(2, 10, by = 1)
y_dgeom <- dgeom(x_dgeom, prob = 0.5)
plot(y_dgeom)


#poisson
set.seed(123)
poisson <- rpois(1000, lambda=3)
plot(poisson, main="A histogram of a Poisson distribution")

#Uniform distribution

rand.unif <- runif(10000, min = -2, max = 0.8)
curve(rand.unif, freq = FALSE, xlab = 'x', density = 20)


#log normal distribution
curve(dlnorm(x, meanlog=0, sdlog=1), from=0, to=25)
//week-3//

# R program to plot gamma distribution
# Specify x-values for gamma function
x_pgamma <- seq(0, 2, by = 0.04)
# Apply pgamma function
y_pgamma <- pgamma(x_pgamma, shape = 6)
# Plot pgamma values
plot(y_pgamma)

//Weibull distribution://
  curve(dweibull(x, shape=2, scale = 1), from=0, to=4,
    main = 'Weibull Distribution (shape = 2, scale = 1)', #add title
    ylab = 'Density', #change y-axis label
    lwd = 2, #increase line width to 2
    col = 'steelblue') #change line color to steelblue
Beta Distribution:

Program:
Plot One Beta Distribution


#define range
p = seq(0,1, length=100)

#create plot of Beta distribution with shape parameters 2 and 10
plot(p, dbeta(p, 2, 10), type='l')


#create custom plot of Beta distribution
plot(p, dbeta(p, 2, 10), ylab='density',
     type ='l', col='purple', main='Beta Distribution')



output:




Plot Multiple Beta Distributions

Program:

#define range
p = seq(0,1, length=100)

#plot several Beta distributions
plot(p, dbeta(p, 2, 10), ylab='density', type ='l', col='purple')
lines(p, dbeta(p, 2, 2), col='red')
lines(p, dbeta(p, 5, 2), col='blue')

#add legend
legend(.7, 4, c('Beta(2, 10)','Beta(2, 2)','Beta(1,1)'),
       lty=c(1,1,1),col=c('purple', 'red', 'blue'))








Triangular Distribution

Description:
To calculate probabilities for the triangular distribution in R we can use the ptri()
function from the EnvStats package, which uses the following syntax:
ptri(q, min = 0, max = 1, mode = 1/2)
where:
• q: Quantile of interest
• min: The minimum value of the distribution
• max: The maximum value of the distribution
• mode: The peak value of the distribution

Example:
Suppose a restaurant estimates that their total sales for the upcoming week will be a minimum of $10,000, a maximum of $30,000, and most likely $25,000. What is the probability that the restaurant makes less than $20,000 total sales?
Program:

library(EnvStats)

#calculate probability
ptri(q = 20000, min = 10000, max = 30000, mode = 25000)

output:

[1] 0.3333333



Calculating Probability Greater Than Some Value

Suppose a shop estimates that the number of customers that will enter in a given week will be a minimum of 500, a maximum of 2,000, and most likely 1,200. What is the probability that more than 1,500 customers enter the shop in a given week?

Program:

library(EnvStats)

#calculate probability
1 - ptri(q = 1500, min = 500, max = 2000, mode = 1200)


Output:
[1] 0.2083333