minor edit in statinf

statinf.tex

@@ -16,9 +16,9 @@ is the evidence of the model $\mathcal{M}$. Bayesian model selection involves co
 Here we solve the curve fitting problem presented in Sec.~\ref{sec:curve_fitting} using of Bayesian statistical inference. 
 
 \begin{enumerate}
-\item Compute the posterior distribution $p(H_0 | d, \mathcal{M}_1)$ of the Hubble constant $H_0$ using the Supernova Cosmology project data $z \leq 0.1$. Assume the Hubble's law [Eq.~\eqref{eq:Hubble_law}] as the model $\mathcal{M}_1$. Assume uniform prior for $H_0$ in the interval $(10, 100)$ km/s/Mpc. You can use a Gaussian likelihood with $\sigma = 1$.  That is, 
+\item Compute the posterior distribution $p(H_0 | d, \mathcal{M}_1)$ of the Hubble constant $H_0$ using the Supernova Cosmology project data $z \leq 0.1$. Assume the Hubble's law [Eq.~\ref{eq:Hubble's Law}] as the model $\mathcal{M}_1$. Assume uniform prior for $H_0$ in the interval $(10, 100)$ km/s/Mpc. You can either use a Gaussian likelihood with $\sigma_{i} = 1$ or calculate the standard deviations (${\sigma_{i}}$) of $d_{L}$ from the data.  In any case, the likelihood of data is:   
 \begin{equation}
-p(d | H_0, \mathcal{M}_1) = \exp \left( - \sum_i \big |d_i - d_L(z_i, \mathcal{M}_1) \big |^2 \right), 
+p(d | H_0, \mathcal{M}_1) = \exp \left( - \sum_i \Big |\dfrac{d_i - d_L(z_i, \mathcal{M}_1)}{\sigma_{i}} \Big |^2 \right), 
 \end{equation}
 where $d_i$ and $z_i$ are the samples of the luminosity distance and redshift from the data and $d_L(z_i, \mathcal{M}_1)$ is the relation between luminosity distance and redshift predicted by model $\mathcal{M}_1$ evaluated at redshift $z_i$. 
 \item Repeat the analysis using the full data set. What are the differences that you see in the posterior?