From 8afad0932064f19b2ecbc7f97b507c800c67fe98 Mon Sep 17 00:00:00 2001
From: aaaakshat <33050725+aaaakshat@users.noreply.github.com>
Date: Thu, 21 Oct 2021 15:42:06 -0400
Subject: [PATCH] Add URM stat functions

---
 ch04.r | 36 ++++++++++++++++++++++++++++++++++++
 1 file changed, 36 insertions(+)

diff --git a/ch04.r b/ch04.r
index 138d3bd..fd93c98 100644
--- a/ch04.r
+++ b/ch04.r
@@ -21,3 +21,39 @@ plot(x, f, type="n")
 lines(x, f, lwd=5)
 plot(x, F, type="n")
 lines(x, F, lwd=5)
+
+# Chapter 4.5
+
+# Generate a uniform random variable
+
+# R code to generate 1000 uniform random numbers
+a = 0; b = 1;
+X = runif(1000, a, b)
+hist(X)
+
+# Mean, variance, median, mode of a uniform random variable
+
+# R code to computer empirical mean, var, median, mode
+library(pracma)
+a = 0; b = 1;
+X = runif(1000, a, b)
+M = mean(X)
+V = var(X)
+Med = median(X)
+Mod = Mode(X)
+
+# R code to compute mean and variance
+unifstat = function(a, b) {
+    M = (a+b)/2
+    V = ((a-b)^2)/12
+    return(list(mean = M, var = V))
+}
+
+a = 0; b = 1;
+M = unifstat(a, b)$mean
+V = unifstat(a, b)$var
+
+# R code to compute the probability P(0.2 < X < 0.3)
+a = 0; b = 1;
+F = punif(0.3, a, b) - punif(0.2, a, b)
+