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,

a. Show that ∫∫ f(x, y) dydx = 1.
b. Find the marginal density function, f₁(x). Do you recognize this distribution?
c. Find the marginal density function, f₂(y). Do you recognize this distribution?

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