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diff --git a/Lectures_my/MC_2016/Lecture8/mchrzasz.pdf b/Lectures_my/MC_2016/Lecture8/mchrzasz.pdf
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diff --git a/Lectures_my/MC_2016/Lecture8/mchrzasz.tex b/Lectures_my/MC_2016/Lecture8/mchrzasz.tex
index 946a323..b50de69 100644
--- a/Lectures_my/MC_2016/Lecture8/mchrzasz.tex
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@@ -309,7 +309,7 @@
 \item Algorithm:
 \begin{enumerate}
 \item We choose first element of the first equation with probability $p$ and second with probability $1-p$.
-\item We we choose the second one, the outcome of this MCMC is $W=A$.
+\item I we choose the second one, the outcome of this MCMC is $W=A$.
 \item If we choose the first we go to second equation and choose the first element with probability $q$ and the second with $1-q$.
 \item We we choose the second one, the outcome of this MCMC is $W=B$.
 \item If we choose the first we go to the first equation back again.
@@ -360,7 +360,6 @@
 \item We are looking at discrete time steps: $1,2,3,...$
 
 
-\item At time $t$ the state is denoted $X_t$.
 \item The conditional probability is defined as:
 \end{itemize}
 \begin{equation}
@@ -373,7 +372,7 @@
 P(X_t=S_j \vert X_{t-1}=S_{j-1},..., X_{1}=S_{1}) =  P(X_t=S_j \vert X_{t-1}=S_{j-1} )\nonumber
 \end{equation}
 \begin{itemize}
-\item For this reason this reason MCMC is also knows as drunk sailor walk.
+\item For this reason MCMC is also knows as drunk sailor walk.
 \item Very powerful method. Used to solve linear eq. systems, invert matrix, solve differential equations, etc.
 \item Also used in physics problems: Brown motions, diffusion, etc.
 \end{itemize}