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?