From 4046210b436fdb3a533bc19bd6d77ea7075e1a00 Mon Sep 17 00:00:00 2001
From: Jan Benda <jan.benda@uni-tuebingen.de>
Date: Mon, 11 Jan 2021 21:41:32 +0100
Subject: [PATCH] [likelihood] fixed exercise
---
likelihood/exercises/likelihood-1.tex | 8 ++++----
1 file changed, 4 insertions(+), 4 deletions(-)
diff --git a/likelihood/exercises/likelihood-1.tex b/likelihood/exercises/likelihood-1.tex
index c0b7f3d..2da6ac2 100644
--- a/likelihood/exercises/likelihood-1.tex
+++ b/likelihood/exercises/likelihood-1.tex
@@ -51,10 +51,10 @@ of the standard deviation.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\question \qt{Maximum-likelihood estimator of a line through the origin}
In the lecture we derived the following equation for an
-maximum-likelihood estimate of the slope $\theta$ of a straight line
+maximum-likelihood estimate of the slope $m$ of a straight line
through the origin fitted to $n$ pairs of data values $(x_i|y_i)$ with
standard deviation $\sigma_i$:
-\[\theta = \frac{\sum_{i=1}^n \frac{x_i y_i}{\sigma_i^2}}{ \sum_{i=1}^n
+\[ m = \frac{\sum_{i=1}^n \frac{x_i y_i}{\sigma_i^2}}{ \sum_{i=1}^n
\frac{x_i^2}{\sigma_i^2}} \]
\begin{parts}
\part \label{mleslopefunc} Write a function that takes two vectors
@@ -105,7 +105,7 @@ normally-distributed data. Such parameter need to be estimated
numerically by means of maximum-likelihood from the data.
Let us demonstrate this approach by means of data that are drawn from a
-gamma distribution,
+gamma distribution.
\begin{parts}
\part Find out which \code{matlab} function computes the
probability-density function of the gamma distribution.
@@ -123,7 +123,7 @@ gamma distribution,
\part Compute and plot a properly normalized histogram of these
random numbers.
- \part Find out which \code{matlab} function fit a distribution to a
+ \part Find out which \code{matlab} function fits a distribution to a
vector of random numbers according to the maximum-likelihood method.
How do you need to use this function in order to fit a gamma
distribution to the data?