The oxygen equivalence number of a weld is a number that can be used to predict properties such as hardness, strength, and ductility. The article;"Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds"; presents several equations for computing the oxygen equivalence number of a weld.

An equation designed to predict the strength of a weld is X = 1.12C + 2.69N + O − 0.21 Fe, where X is the oxygen equivalence, and C, N, O, and Fe are the amounts of carbon, nitrogen, oxygen, and iron, respectively, in weight percent, in the weld. Suppose that for welds of a certain type, \(\mu;C=0.0247,\mu;N=0.0255,\mu;o=0.1668,\mu;Fe=0.0597,\sigma;C=0.0131,\sigma;N=0.0194,\sigma;o=0.0340, and\ \sigma;Fe=0.0413.\)

Furthermore assume that correlations are given by \(\rho;C,N=\min;0.44,\rho;C,O=0.58,\rho;C,Fe=0.39,\rho;N,O=\min;0.32,\rho;N,Fe=0.09, and\ \rho;O.Fe=\min;0.35.\)

a. Find \(\mu;x\).

b. Find Cov(C, N), Cov(C, O), Cov(C, Fe), Cov(N, O), Cov(N, Fe), and Cov(O, Fe).

c. Find \(\sigma;X\). .