From bf80da15a9a783ed55270a3a98954a501ef233f2 Mon Sep 17 00:00:00 2001
From: SowinskiBraeden <braeden@sowinski.dev>
Date: Thu, 9 Apr 2026 11:15:13 -0700
Subject: [PATCH] lab 09

---
 lab09.R | 124 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 124 insertions(+)
 create mode 100644 lab09.R

diff --git a/lab09.R b/lab09.R
new file mode 100644
index 0000000..c11588c
--- /dev/null
+++ b/lab09.R
@@ -0,0 +1,124 @@
+set.seed(123)
+
+# Q1
+NormalMeans = function(n, m)
+{
+  means <- c(1:n)
+  
+  for (i in 1:n)
+  {
+    values <- rnorm(m, mean = 0, sd = 1)
+    means[i] <- mean(values)
+  }
+  
+  title <- paste(n, "sample means from N(0,1) with sample size", m)
+  hist(means, main = title, xlab = "Sample mean", ylab = "Frequency")
+  
+  return(c(mean(means), sd(means)))
+}
+
+normal_m1 <- NormalMeans(10000, 1)
+normal_m2 <- NormalMeans(10000, 2)
+normal_m10 <- NormalMeans(10000, 10)
+normal_m50 <- NormalMeans(10000, 50)
+normal_m100 <- NormalMeans(10000, 100)
+
+normal_m1
+normal_m2
+normal_m10
+normal_m50
+normal_m100
+
+# Q2
+ExponentialMeans = function(n, m)
+{
+  means <- c(1:n)
+  
+  for (i in 1:n)
+  {
+    values <- rexp(m, rate = 1)
+    means[i] <- mean(values)
+  }
+  
+  title <- paste(n, "sample means from Exp(1) with sample size", m)
+  hist(means, main = title, xlab = "Sample mean", ylab = "Frequency")
+  
+  return(c(mean(means), sd(means)))
+}
+
+exp_m1 <- ExponentialMeans(10000, 1)
+exp_m2 <- ExponentialMeans(10000, 2)
+exp_m10 <- ExponentialMeans(10000, 10)
+exp_m50 <- ExponentialMeans(10000, 50)
+exp_m100 <- ExponentialMeans(10000, 100)
+
+exp_m1
+exp_m2
+exp_m10
+exp_m50
+exp_m100
+
+# Q3
+ExponentialMeansProb = function(n, m, z)
+{
+  means <- c(1:n)
+  
+  for (i in 1:n)
+  {
+    values <- rexp(m, rate = 1)
+    means[i] <- mean(values)
+  }
+  
+  probability <- mean(means >= (1 - z) & means <= (1 + z))
+  return(probability)
+}
+
+prob_2_1 <- ExponentialMeansProb(10000, 2, 1)
+prob_2_05 <- ExponentialMeansProb(10000, 2, 0.5)
+prob_2_02 <- ExponentialMeansProb(10000, 2, 0.2)
+
+prob_5_1 <- ExponentialMeansProb(10000, 5, 1)
+prob_5_05 <- ExponentialMeansProb(10000, 5, 0.5)
+prob_5_02 <- ExponentialMeansProb(10000, 5, 0.2)
+
+prob_10_1 <- ExponentialMeansProb(10000, 10, 1)
+prob_10_05 <- ExponentialMeansProb(10000, 10, 0.5)
+prob_10_02 <- ExponentialMeansProb(10000, 10, 0.2)
+
+prob_2_1
+prob_2_05
+prob_2_02
+prob_5_1
+prob_5_05
+prob_5_02
+prob_10_1
+prob_10_05
+prob_10_02
+
+# Q4
+library(MASS)
+
+data(genotype)
+
+groupA <- subset(genotype, Litter == "A")
+groupB <- subset(genotype, Litter == "B")
+groupI <- subset(genotype, Litter == "I")
+groupJ <- subset(genotype, Litter == "J")
+
+qqnorm(groupA$Wt, main = "QQ Plot of Weight for Litter Genotype A")
+qqline(groupA$Wt)
+
+qqnorm(groupB$Wt, main = "QQ Plot of Weight for Litter Genotype B")
+qqline(groupB$Wt)
+
+qqnorm(groupI$Wt, main = "QQ Plot of Weight for Litter Genotype I")
+qqline(groupI$Wt)
+
+qqnorm(groupJ$Wt, main = "QQ Plot of Weight for Litter Genotype J")
+qqline(groupJ$Wt)
+
+# Optional support if you want a numerical check as well
+shapiro.test(groupA$Wt)
+shapiro.test(groupB$Wt)
+shapiro.test(groupI$Wt)
+shapiro.test(groupJ$Wt)