26. The first step in the decision-making process of chapter 7, is to identify and define the problem.

27. Creativity is one of our greatest personal assets, even though it may not be recognized.

28. Step 3 of the decision-making process, making a decision, is the easiest of the four steps in this process.

29. The Mount Everest case in chapter 7, illustrates the do ethical reasoning for all of the steps of the decision-making process.

30. Self-confidence means you do not need others as team members to succeed at work.

1. Explain why one would use a probability density function rather than a probability function to quantify the uncertainty of a specific measurand. 2. Explain the main difference between a normalized Gaussian function and a standard Gaussian function.(1 point) The following function is called a Gaussian Function. Gaussian functions are used in statistics, Image processing, signal processing, and in mathematics to solve heat and diffusion equations. f(s) - de Find the first and second derivative of the given Gaussian function when a = 3, b = 1, and c == 3 f'(z) = -(x-1) ((2e)~(-((x-1)*2)/(9)>(3)) f" (=) = -((2e)~(-((x-1)"2)(9))(-2x*2+4x+7))/(27) NOTE: It will be much easier to type your answer if you simplify the derivative functions (but is not necessary). Hint:It's are not allowed. Please do write in such a way that we we points to unintelligible scribbles. problems on three pages. In total you can earn with this part of the test 60 points. Points are assigned as indicated. There are sis Please read this notice: START EACH PROBLEM ON A NEW PAGE Problems: 1. (15) A projection X-ray imaging system is set up as shown in Figure I. All length units are in cmn. Object Source W z = 40/ /Detector d = 60 Figure | Projection radiography system problem 1. Assume that the total system response can be described by the following convolution: L(x,, VJ) = Ks(x, / m. y. Im).(x, IM, y,IM) . where xy denote coordinates in the detector plane, K is a constant, s(x, y) denotes the X-ray source distribution and /(xy) is the spatial transmission function of the object whose thickness we ignore, and i and M are the source and object magnification, respectively. Assume that the X-ray source can be described as a ID Gaussian function: s(x, y) = Sge 6(y) (a) (5) Compute the object magnification M/ and the source magnification m. Answer Object magnification M = Sze image size object 3 40 50 = 1.5 Source magnification follows from placing a pinhole at the position of the object, source diameter D, imaged via pinhole at image plane diameter D': D -D' D' d- z D D -=1-M = -0.5 Z An ideal line phantom is to be imaged by the system, whose transmission function is given by