1 a type of structure of an organism or part of an organism in which a vertical cut through the axis in any of two or more planes produces two halves that are mirror images of each other.2  Compare bilateral symmetry. Trends. 2  a type of structure of an organism or part of an organism in which a vertical cut through the axis in any of two or more planes produces two halves that are mirror images of each other.
What distribution does X/(X+Y), follow, when X and Y are gamma distributed. Prove that the R.V is independent of (X+Y) up vote 0 down vote favorite. What distribution does the following r.v follow: X/(X+Y) Xâ¼Gamma(a,1) Yâ¼Gamma(b,1) and the variables are independent.
Here is a sketch of the answer: Define V=X+Y=g1(X,Y) and U=XX+Y=g2(X,Y), then compute the joint density fU,V(u,v)=fX(gâ12(u,v))fY(gâ12(u,v))|J|=Gamma(a+b,1)Beta(a,b), where J is the Jacobian of the change of variables J=|vuâv1âu|=v. Now, you can get that fU(u)=â«R+fU,Vdv=Beta(a,b).