# Risk Assessment of Fixed Obstacles along Roads
## 6 Definition of Mathematical Assignment  
The solved problem operates with the values of the measured quantities understood as random processes dependent on time t [s]. The modelled quantity \(y_{t}\) represents the integral accident rate (\(R_{z}\)), which can be described as a discrete random process. Because of the required transformation of the calculated accident severity \(R_{z}\) into the society-wide road traffic risk \(y_{t}\), four accident severity intervals are observed. Table 3 shows the correlation between the variables \(R_{z}\) and \(y_{t}\). Furthermore, the table provides information on which specific values of these two parameters correspond to the individual characteristics of the consequences of traffic accidents [18]. The section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn. In order to test the hypothesis, it is assumed that the subject severity is influenced by the independent variables \(x_{1,t}\), \(x_{2,t}\),... \(x_{nct}\). These parameters can be described as discrete variables taking only a finite number of different values. Specifically, the four independent variables mentioned earlier were selected:  
\(x_{1}\)**- the relative height position of the road level and the fixed obstacle; \(x_{2}\)**- the effect of a road ditch on vehicle deceleration; \(x_{3}\)**- spatial routing; \(x_{4}\)**- the distance of the fixed obstacle from the road. The verification of the stated hypothesis consists in comparing the assumptions defined in Table 1 with what is recorded in the accident event. The following tables, based on information based on the accident events, will be obtained by analyzing the probability function (pf) of all the variables considered:  
\[p(x,y)=p(x_{1},x_{2},x_{3},x_{4},y), \tag{5}\]  
where \(x_{1},x_{2},x_{3},x_{4}\) are the observed independent variables and \(y\ \in\{1,2,3,4\}\) are the intervals of the integral accident rate \(R_{z}\), respectively, the severity of the fixed obstacle in road traffic. \begin{table}
\begin{tabular}{c c c} \hline \hline \(R_{z}\) & \multicolumn{2}{c}{**Number of Traffic Accidents**} \\ \hline
**[Consequence Index/10,000 Vehicles per Day]** & \(\sum\) & \% \\ \hline (0–5\(\geq\) & 71 & 25.36 \\ \hline (5–10\(\geq\) & 64 & 22.86 \\ \hline (10–25\(\geq\) & 77 & 27.50 \\ \hline More than 25 & 68 & 24.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Defined intervals \(R_{z}\) and their corresponding frequency and percentage of individual records. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{\(R_{z}\)} & \multicolumn{3}{c}{**Level of Severity in Road Traffic**} \\ \cline{2-4}  & \(y_{t}\) & **Risk Level** & **Specification** \\ \hline (0–5\(\geq\) & 1 & Without Risk & Only material damage will be caused \\ \hline (5–10\(\geq\) & 2 & Low Risk & No more than a slight injury \\ \hline (10–25\(\geq\) & 3 & Medium Risk &
\begin{tabular}{c} Always a slight injury, but no serious \\ injuries are recorded \\ \end{tabular} \\ \hline More than 25 & 4 & High Risk & Severe or fatal injuries \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Interrelations between the variables \(R_{z}\) and y. The properties of this function, which also contains the searched dependencies, are indicated by the created data file. This pooled probability function is first decomposed into the product of the conditional and marginal pooled probability functions:  
\[p(x_{1},x_{2},x_{3},x_{4},y)=p(y)\cdot p(y), \tag{6}\]  
where the marginal \(p(y)\) reveals the total frequencies of individual traffic accidents located within the defined intervals of \(R_{z}\) (see Table 3), but does not provide information about the relationship x and y. In contrast, the conditional pf \(p(y)\) is of interest.