abarS := (-2 thB +
2 thB^2 xi + \[Sqrt]((2 thB - 2 thB^2 xi)^2 -
4 (-thB + thB^2 xi) (2 - 2 thB - xi - 2 thB xi + 3 thB^2 xi +
2 thB xi^2 - 2 thB^2 xi^2 + 2 thB Log[thB] -
4 thB xi Log[thB] - 2 thB^2 xi Log[thB] +
2 thB xi^2 Log[thB] + 4 thB^2 xi^2 Log[thB] -
2 thB^2 xi^3 Log[thB] + 2 thB Log[1 - xi] -
4 thB xi Log[1 - xi] - 2 thB^2 xi Log[1 - xi] +
2 thB xi^2 Log[1 - xi] + 4 thB^2 xi^2 Log[1 - xi] -
2 thB^2 xi^3 Log[1 - xi] - 2 thB Log[1 - thB xi] +
4 thB xi Log[1 - thB xi] + 2 thB^2 xi Log[1 - thB xi] -
2 thB xi^2 Log[1 - thB xi] -
4 thB^2 xi^2 Log[1 - thB xi] +
2 thB^2 xi^3 Log[1 - thB xi])))/(2 (2 - 2 thB - xi -
2 thB xi + 3 thB^2 xi + 2 thB xi^2 - 2 thB^2 xi^2 +
2 thB Log[thB] - 4 thB xi Log[thB] - 2 thB^2 xi Log[thB] +
2 thB xi^2 Log[thB] + 4 thB^2 xi^2 Log[thB] -
2 thB^2 xi^3 Log[thB] + 2 thB Log[1 - xi] -
4 thB xi Log[1 - xi] - 2 thB^2 xi Log[1 - xi] +
2 thB xi^2 Log[1 - xi] + 4 thB^2 xi^2 Log[1 - xi] -
2 thB^2 xi^3 Log[1 - xi] - 2 thB Log[1 - thB xi] +
4 thB xi Log[1 - thB xi] + 2 thB^2 xi Log[1 - thB xi] -
2 thB xi^2 Log[1 - thB xi] - 4 thB^2 xi^2 Log[1 - thB xi] +
2 thB^2 xi^3 Log[1 - thB xi]));
xbar := abarS*xi*(1 - thB)/(1 - xi*thB);
c := 1/(abarS*xi*(1 - thB) + xi*thB -
abarS*thB*xi*(1 - xi)*Log (thB*(1 - xi)/(1 - xi*thB)));
f1[x_, thB_, xi_] :=
Piecewise[{{c*(1 - abarS*thB*xi*(1 - xi)/(abarS*xi - x)),
0 <= x <= xbar}, {xbar <= x <= 1, c*xi*thB}}, 0]
jointf1[x1_, x2_, thB_, xi_] :=
Piecewise[{{1 >= x1 > x2, 2*f1[x1, thB, xi]*f1[x2, thB, xi]}}, 0];
jointd1[a1_, a2_] :=
Integrate[jointf1[x1, x2], {x2, 0, a2}, {x1, 0, a1},
Assumptions ->
0 < thB < 1 && 0 < xi < 1 && 0 < xbar < 1 && 0 < abarS < 1];
Plot3D[jointf1[x1, x2, 0.5, 0.91], {x1, 0, 1}, {x2, 0, 1}]
Thank you for your reply.
Let me explain: abarS, xbar and c are expressions of thB and xi. And jointf1 is defined as a function of four variables.
But when I try to plot the jointf1 with thB=0.5, xi=0.91, the code gives empty plot. Is there a problem in my code?
Thanks again!