Laboratory 2 Assignment Mozart St. Brun

rm()

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Functions

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# --- Functions ---
FlipCoin <- function(n) sample(0:1, n, rep=TRUE)
RollDie <- function(n) sample(1:6, n, rep=TRUE)

# --- Coin Toss: 100 tosses ---
set.seed(1)
coin_100 <- FlipCoin(100)
coin_100_table <- table(coin_100)
coin_100_rel <- prop.table(coin_100_table)

# --- Coin Toss: 100 tosses ---
set.seed(1)
coin_100 <- FlipCoin(100)
coin_100_table <- table(coin_100)
coin_100_rel <- prop.table(coin_100_table)

# --- Coin Toss: 500 tosses ---
coin_500 <- FlipCoin(500)
coin_500_table <- table(coin_500)
coin_500_rel <- prop.table(coin_500_table)

# --- Coin Toss: 500 tosses ---
coin_500 <- FlipCoin(500)
coin_500_table <- table(coin_500)
coin_500_rel <- prop.table(coin_500_table)

# --- Die Roll: 200 rolls ---
set.seed(2)
die_200 <- RollDie(200)
die_200_table <- table(factor(die_200, levels = 1:6))
die_200_rel <- prop.table(die_200_table)

# --- Die Roll: 1000 rolls ---
die_1000 <- RollDie(1000)
die_1000_table <- table(factor(die_1000, levels = 1:6))
die_1000_rel <- prop.table(die_1000_table)

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Histograms

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# --- Histograms ---
hist(coin_100,
     breaks = c(-0.5, 0.5, 1.5),
     prob = TRUE,
     col = c("skyblue", "salmon"),
     xlab = "Outcome (0 = Tails, 1 = Heads)",
     main = "Mozart St. Brun: Coin Tosses (100)")

hist(die_200,
     breaks = seq(0.5, 6.5, by=1),
     prob = TRUE,
     col = "lightgreen",
     xlab = "Die Face",
     main = "Mozart St. Brun: Die Rolls (200)")

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Final Output Table

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# --- Relative Frequency Tables ---

# Coin results
coin_table <- data.frame(
  Outcome = c("Tails (0)", "Heads (1)"),
  RelFreq_100 = as.numeric(coin_100_rel),
  RelFreq_500 = as.numeric(coin_500_rel)
)

# Die results
die_table <- data.frame(
  Face = 1:6,
  RelFreq_200 = as.numeric(die_200_rel),
  RelFreq_1000 = as.numeric(die_1000_rel)
)

# Show tables
cat("\nRelative Frequency Table: Coin Tosses\n")

Relative Frequency Table: Coin Tosses

print(coin_table, row.names = FALSE)

cat("\nRelative Frequency Table: Die Rolls\n")

Relative Frequency Table: Die Rolls

print(die_table, row.names = FALSE)