deletions | additions       diff --git a/subsection_Approximation_of_probability_distribution__.tex b/subsection_Approximation_of_probability_distribution__.tex  index 246172d..a395c00 100644  --- a/subsection_Approximation_of_probability_distribution__.tex  +++ b/subsection_Approximation_of_probability_distribution__.tex 
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in another words $p(x,y)$ is given by:  \[P_{hist}((x,y),T) = \sum_{(x',y')\in T}\mathbb{1}_{(x=x',y=y')}\]  Similarly the histogram of joint distribution of two trajectories $T$ and $S$ will be is  given by: \[P_{hist}((x_{1},y_{1},x_{2},y_{2}),TxS) = \sum_{(x'_{1},y'_{1},x'_{2},y'_{2})\in TxS}\mathbb{1}_{((x_{1}=x'_{1},y_{1}=y'_{1},x_{2}=x'_{2},y_{2}=y'_{2}))}\] TxS}\mathbb{1}_{(x_{1}=x'_{1},y_{1}=y'_{1},x_{2}=x'_{2},y_{2}=y'_{2})}\]