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begin{align*}
f_{y_1,y_2} (y_1,y_2) &= f__{X_1,X_2}(y_1, frac{(1-y_1)}{2} - sqrt{ frac{y_2}{2} -frac{{y_1}^{2}}{2} - frac{(1-y_1)^{2}}{4}} ) abs {J_1}
+ f__{X_1,X_2}(y_1, frac{(1-y_1)}{2} + sqrt{ frac{y_2}{2} -frac{{y_1}^{2}}{2} - frac{(1-y_1)^{2}}{4}} ) abs {J_2}
f_{y_1,y_2} (y_1,y_2) & = frac{Gamma(alpha_1 +alpha_2)}{Gamma(alpha_1) Gamma(alpha_2)} vast[ (frac{(1-y_1)}{2} - sqrt{R})^{alpha_2 -1} + ( frac{(1-y_1)}{2}+ sqrt{R})^{alpha_2 -1} vast]
end{align*}
I do not where the problem is. Thank you so much for your help.









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    begin{align*}
    f_{y_1,y_2} (y_1,y_2) &= f__{X_1,X_2}(y_1, frac{(1-y_1)}{2} - sqrt{ frac{y_2}{2} -frac{{y_1}^{2}}{2} - frac{(1-y_1)^{2}}{4}} ) abs {J_1}
    + f__{X_1,X_2}(y_1, frac{(1-y_1)}{2} + sqrt{ frac{y_2}{2} -frac{{y_1}^{2}}{2} - frac{(1-y_1)^{2}}{4}} ) abs {J_2}
    f_{y_1,y_2} (y_1,y_2) & = frac{Gamma(alpha_1 +alpha_2)}{Gamma(alpha_1) Gamma(alpha_2)} vast[ (frac{(1-y_1)}{2} - sqrt{R})^{alpha_2 -1} + ( frac{(1-y_1)}{2}+ sqrt{R})^{alpha_2 -1} vast]
    end{align*}
    I do not where the problem is. Thank you so much for your help.









    share







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      begin{align*}
      f_{y_1,y_2} (y_1,y_2) &= f__{X_1,X_2}(y_1, frac{(1-y_1)}{2} - sqrt{ frac{y_2}{2} -frac{{y_1}^{2}}{2} - frac{(1-y_1)^{2}}{4}} ) abs {J_1}
      + f__{X_1,X_2}(y_1, frac{(1-y_1)}{2} + sqrt{ frac{y_2}{2} -frac{{y_1}^{2}}{2} - frac{(1-y_1)^{2}}{4}} ) abs {J_2}
      f_{y_1,y_2} (y_1,y_2) & = frac{Gamma(alpha_1 +alpha_2)}{Gamma(alpha_1) Gamma(alpha_2)} vast[ (frac{(1-y_1)}{2} - sqrt{R})^{alpha_2 -1} + ( frac{(1-y_1)}{2}+ sqrt{R})^{alpha_2 -1} vast]
      end{align*}
      I do not where the problem is. Thank you so much for your help.









      share







      New contributor




      MathMan12 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.












      begin{align*}
      f_{y_1,y_2} (y_1,y_2) &= f__{X_1,X_2}(y_1, frac{(1-y_1)}{2} - sqrt{ frac{y_2}{2} -frac{{y_1}^{2}}{2} - frac{(1-y_1)^{2}}{4}} ) abs {J_1}
      + f__{X_1,X_2}(y_1, frac{(1-y_1)}{2} + sqrt{ frac{y_2}{2} -frac{{y_1}^{2}}{2} - frac{(1-y_1)^{2}}{4}} ) abs {J_2}
      f_{y_1,y_2} (y_1,y_2) & = frac{Gamma(alpha_1 +alpha_2)}{Gamma(alpha_1) Gamma(alpha_2)} vast[ (frac{(1-y_1)}{2} - sqrt{R})^{alpha_2 -1} + ( frac{(1-y_1)}{2}+ sqrt{R})^{alpha_2 -1} vast]
      end{align*}
      I do not where the problem is. Thank you so much for your help.







      errors





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      MathMan12 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      share



      share






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      asked 4 mins ago









      MathMan12MathMan12

      82




      82




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