need an article which include a decision making process for such a company and that decision must include the fundamentals of the decision making process which are as the following:

1- setting the right frame work

2- considering alternatives

3-gathering meaningful data

4-clarifying values and tradeoffs

5-using logical reasoning

6- committing to action

3. A test for multivariate normality is to be conducted. Instead of looking at the whole Ill-Q olotr we look at only one quantile. {a} (4 points} If a random 'vector .1: Follows the multivariate normal distribution Npl. 2}. nd the value of Cr. such that P{x IE W11: p]'E\"{x p11: 5\"} = l a. {h} {6 points} Esaunre that for a 5am ole of n = 1m observations, we find that there are at} observations satisfy [to - i]'5"{3t.- - i] 5 mm. where i is the sample mean vector and S is the sample oovarianoe matrix. The dimension of 1:.- is 3 a: 1. Whether the sample follows a multivariate normal distribution? Explain the reason. 7. Consider the matrix A = ( ] ], ) (a) (10 points) Find the spectral decomposition of A. (b) (10 points) Find an orthogonal matrix P and a diagonal matrix D such that PT AP = D. If {un,...,un} is an orthonormal basis for R" consisting of cigenvectors of A, and Al, ...; An are the corresponding eigenvalues, then the spectral decomposition of A is defined byPRoBLEM 10.4 A chemical solution contains N molecules of type A and an equal number of molecules of type B. A reversible reaction occurs between type A and B molecules in which they bond to form a new compound AB. Suppose that in any small time interval of length h, any particular unbonded A molecule will react with any particular unbonded B molecule with probability och + O[h), where or is a reaction rate of formation. Suppose also that in any small time interval of length hI any particular AB molecule disassociates into its A and B constituents with probability ll + DUI), where fl is a reaction rate of dissolution. Let X (t) denote the number of AB molecules at time t. Model X(t} as a birth and death process by specifying the parameters. Note that one mole of molecules is N = 6.02214129 X 1023