# include = FALSE
library(tidyverse)
library(kableExtra)


# echo = FALSE
# boxplot
bp<- data.frame(blpr = c(118, 144, 134, 110, 119, 128, 132, 136, 125, 160, 190, 140, 150, 160, 220,100, 70, 90, 75, 110, 115, 108, 50, 111, 110, 60, 80, 70, 40, 60), time = rep(c("before", "after"), each = 15))
boxplot(blpr~time, 
        horizontal = T, 
        main = "Systolic Blood Pressures", 
        data = bp,
        col = "orchid")



# echo=FALSE
set.seed(3516)
hist(rgamma(999, 6, 1), main = "Practice Histogram", xlab = "mystery data", col = "skyblue1")


# echo=FALSE
set.seed(17)
classicaltime <- rnorm(20,50,10)
testscores <- classicaltime + rnorm(20, 30, 9)
mod <- lm(testscores~classicaltime)


# echo=FALSE
cat("Mean Time Listening to Classical Music:", signif(mean(classicaltime),4))
cat("\nMean Test Scores:", signif(mean(testscores),4))
cat("\nStd Dev of Time Listening to Classical Music:", signif(sd(classicaltime), 3))
cat("\nStd Dev of Test Scores:", signif(sd(testscores),3))
cat("\nCorrelation:", signif(cor(classicaltime,testscores),4))
cat("\nRegression Line Slope:", signif(mod$coefficients[[2]]))


# echo = FALSE
library(tidyverse)
library(kableExtra)
tab4 <- data.frame(Disease = c("Present", "Absent", "Total"),
                   Positive = c(2970, 11000, 13970),
                   Negative = c(30,539000, 539030),
                   Total = c(3000, 550000, 553000))
kable(tab4) %>%
  kable_styling(bootstrap_options = c("striped", "hover")) %>%
  add_header_above(c(" " = 1, "Test Result" = 2, " " = 1))



# 
# Setting our values
n <- 3
x <- 2
p <- 1/3

# Manually using the binomial formula:
factorial(n)/(factorial(x)*factorial(n-x)) * p^x * (1-p)^(n-x)

# You can also do this using the 'choose' function:
choose(n, x)* p^x * (1-p)^(n-x)


# 
dbinom(x = 2, size = 3, prob = 1/3)


# 
# Manually using the binomial formula:
factorial(10)/(factorial(5)*factorial(10-5)) * (1/3)^5 * (1-(1/3))^(10-5)

# Using the dbinom function:
dbinom(x = 5, size = 10, prob = 1/3)


# 
# The probability of picking 1 or less potatoes (1 potato or 0 potatoes)
pbinom(1, size = 10, prob = 1/3)

# The probability of picking 5 or more potatoes (5, 6, 7, 8, 9, or 10 potatoes)
# Note that instead of x = 5, we use x = 4
1 - pbinom(4, size = 10, prob = 1/3) 

# Alternatively, using the lower.tail argument:
pbinom(4, size = 10, prob = 1/3, lower.tail = F)

# Total of the Extremes:
pbinom(1, size = 10, prob = 1/3) + (1 - pbinom(4, size = 10, prob = 1/3))



# 
# The probability of picking 5 or more potatoes (5, 6, 7, 8, 9, or 10 potatoes)
dbinom(5, size = 10, prob = 1/3) + 
  dbinom(6, size = 10, prob = 1/3) + 
  dbinom(7, size = 10, prob = 1/3) +
  dbinom(8, size = 10, prob = 1/3) +
  dbinom(9, size = 10, prob = 1/3) +
  dbinom(10, size = 10, prob = 1/3)


# 
binom.test(x=5, n=10, p=1/3)