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" (D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s-136s) 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, μc = 0.0247, μN = 0.0255, μ0 = 0.1668, ,μFe = 0.0597, σc = 0.0131, σN = 0.0194, σO = 0.0340, and σFe = 0.0413. Furthermore assume that correlations are given by ρC,N = -0.44, ρC,O = 0.58, ρC,Fe = 0.39, ρN,O = -0.32, ρN,Fe = 0.09, and ρO,Fe = -0.35.

a. Find μX.

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

c. Find σX.

Step 1 of 4:

Here an equation designed to measure the strength of a weld is given.

The equation is X=1.12C+2.69N+O-0.21Fe, where X is the oxygen equivalence,C stands for amount of carbon,N stands for amount of nitrogen, O stands for amount of oxygen,Fe stands for amount of iron.

Also,the means of the amounts of C,N,O and Fe are given.

=0.0255

=0.0597

Standard deviations of C,N,O and Fe are

=0.0131

=0.0194

=0.0340

=0.0413

The correlations between C,N,O and Fe are also given as

=-0.44

=0.58

=0.39

=-0.32

=0.09

=-0.35

Using these given values we have to find the required values.