Bardzo prosilabym o pomoc kogos dobrego serca bede wdzieczna....
\(\displaystyle{ X = (X_{1},X_{2}) \sim f_{x}(X_{1},X_{2}) = \begin{cases} X_{1}+X_{2}, dla X_{1} , X_{2} \in (0,1)\\0 , poza tym \end{cases}}\)
a) znalezc dystrybuante wektora \(\displaystyle{ X}\) :
\(\displaystyle{ F_{x} (X_{1},X_{2}) = P (X_{1} \le x_{1} , X_{2} \le x_{2})}\)
b) znalezc gęstości brzegowe dla \(\displaystyle{ X_{1} , X_{2}}\) :
\(\displaystyle{ f_x{1}(x_{1}) = \int\limits_{R} f_{x}(X_{1},X_{2})dx_{2}}\)
c)Znaleźć \(\displaystyle{ A = Y \cdot A \cdot X}\)
\(\displaystyle{ Y = (Y_{1},Y_{2}) , Y_{1}=X_{1} , Y_{2}=X_{1}+X_{2}}\)
\(\displaystyle{ f_{y}(y_{1},y_{2})}\) - gestosc laczna
d) \(\displaystyle{ f_{y_{2}}(y_{2})=f_{X_{1}+X_{2}}(y_{2}) = ?}\) - jako gestosc brzegowa wektora \(\displaystyle{ (Y_{1},Y_{2})}\)
e) gestosc warunkowa: \(\displaystyle{ X_{2} | X_{1} = 1/2}\)
\(\displaystyle{ f_{x_{1}|X_{2}}=1/2 (X_{1}|1/2)=\frac{f_X_{1},X_{2}(X_{1},1/2)}{f_{x_{2}}(1/2)}}\)
f) warunkowa wartosc oczekiwana znalezc... :
\(\displaystyle{ E[X_{2}|X_{1}=1/2] = \int x_{1} \cdot f_X_{1}|X_{2}} = 1/2(X_{1}|1/2)dx_{1}}\)-- 7 lis 2010, o 20:27 --nikt nie pomoze w jakimkolwiek podpunkcie?:(