1: Filtering for Probabilites.

The following code will load the Titanic data set as a training set and a testing set.

library("tidyverse")
library("titanic")

train_df <- titanic_train #training set of Titanic data
test_df <- titanic_test #testing set of Titanic data

Use R to compute the following probabilities.

  1. Based on the training set sample, what is the probability that a randomly selected passenger was both in first class or whose age \(\leq\) 35?
N <- nrow(train_df) #number of passangers in the data set

train_df %>%
  filter(Pclass == 1 | Age == 35) %>%
  summarize(prob = n() / N) #counts the rows
##        prob
## 1 0.2525253
  1. Based on the testing set sample, what is the probability that a randomly selected passenger was both in second class and whose age \(>\) 35?
N <- nrow(test_df) #number of passangers in the data set

test_df %>%
  filter(Pclass == 2 | Age == 35) %>%
  summarize(prob = n() / N) #counts the rows
##        prob
## 1 0.2320574

2: Coin Simulations

Starting with the following code, run a simulation and make a ggplot barplot for the a. distribution of one coin flip

library("ggplot2")
coin <-  c("heads", "tails")

one_coin <- sample(coin, 1, replace = TRUE)
simulation <-replicate(10000, sample(coin, 1, replace = TRUE))
df <- data.frame(simulation)

ggplot(df, aes(x = simulation)) + 
  geom_bar() + ggtitle("Ditribution of one coin flip") + theme(axis.text.x = element_text(angle = 270, vjust = 0.33))

  1. distribution of two coin flips
two_coins <- paste(sample(coin, 2, replace = TRUE), collapse = " ")
simulation <- replicate(10000, paste(sample(coin, 2, replace= TRUE), collapse = " "))
df <- data.frame(simulation)

ggplot(df, aes(x = simulation)) + 
  geom_bar() + ggtitle("Ditribution two coins") + theme(axis.text.x = element_text(angle = 270, vjust = 0.33))

c. distribution of three coin flips

three_coins <- paste(sample(coin, 3, replace = TRUE), collapse = " ")
simulation <- replicate(10000, paste(sample(coin, 3, replace= TRUE), collapse = " "))
df <- data.frame(simulation)

ggplot(df, aes(x = simulation)) + 
  geom_bar() + ggtitle("Ditribution three coins") + theme(axis.text.x = element_text(angle = 270, vjust = 0.33))

library("ggplot2")
coin <- c("heads", "tails")


#one_coin <- sample(coin, 1)
#two_coins <- paste(sample(coin, 2, replace = TRUE), collapse = " ")
#three_coins <- paste(sample(coin, 3, replace = TRUE), collapse = " ")

Be sure to use ggtitle to put a title on each graph, and add a layer such as theme(axis.text.x = element_text(angle = 270, vjust = 0.33)) to fix the axis’ labels.

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