Refer to the Journal of Engineering Mechanics (Dec. 2009) study of the characteristics of a 10-bar truss subjected to loads, Exercise 6.13. Recall that the joint probability distribution of stiffness index X (pounds/sq. in.) and load Y (thousand pounds) is given by the formula,    

The square root of the load Y is an important variable for determining the level of stress the truss is able to withstand. Let W = √Y . Find the probability density function for W. Then show that ∫ f (w)dw = 1.

Data from Exercise 6.13

In building construction, a truss is a structure comprised of triangular units whose ends are connected at joints referred to as nodes. The Journal of Engineering Mechanics (Dec. 2009) published a study of the characteristics of a 10-bar truss subjected to loads at four different nodes. Two random variables measured were stiffness index (pounds per square inch) and load (thousand pounds). One possible joint probability distribution of stiffness index X and load Y is given by the formula

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f(x, y) = (1/40)e,0