p=4 alpha(x-side)  convex in sigma=1/X in all 169 cases: True  fails=0 []
p=4 E(X,Y)         convex in sigma=1/X in all 169 cases: False  fails=105 [(0.0001, 2150.0), (0.0001, 4640.0), (0.0001, 10000.0), (0.000464, 464.0), (0.000464, 1000.0)]
p=4 beta(y-side)   convex in sigma=1/X in all 169 cases: True  fails=0 []
p=4 E(X,Y)+beta    convex in sigma=1/X in all 169 cases: True  fails=0 []
p=4 alpha+E(X,Y)   convex in sigma=1/X in all 169 cases: True  fails=0 []
p=4 H total        convex in sigma=1/X in all 169 cases: True  fails=0 []
