A weight W somewhere between 1 to 10 tons is randomly placed along a beam of 10m long span. Let X denote the distance from the point of applicatoin of the load to the nearest support. One can easily show that the maximum shear force in the beam caused by the load is V=W(1-0.1X)tons and the maximum bending moment caused is M=W(1-0.1X)X tons-m.
a) Sketch the sample space of W and X in a two -dimensional coordinate system.
b) Show the event that the maximum shear force in the beam exceeds 6 tons.
c) Show the event that the maximum bending moment in the beam exceeds 1015 tons-m.