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- A ray of light is incident on an air/water interface. The ray makes an angle of θ1 = 18 degrees with respect to the normal of the surface. The index of the air is n1 = 1 while water is n2 = 1.33. Choose an expression for the angle (relative to the normal to the surface) for the ray in the water, θ2 .
- Calculate the area of the following triangle. A triangle with an angle marked 55 degrees and the sides either side of it marked 7 metres and 6 metres. Enter your answer in square metres rounded to one decimal place in the box below. (Your answer should be a number, without units.)
- Consider the following data set with n = 7 observations and p = 3 variables. The data set is given next. V1 V 2 V 3 A 4.7 4.2 2 B 4.7 6.3 0.8 C 6.2 4.2 1 D 5.9 3.9 0.8 E 0.9 2.8 4 F 4.3 3 4.2 G 2.3 5.7 1.7 C) Using the above data X , the R command KM<-kmeans(x=X,centers=3) was run, with the following output > KM$cluster [1] 1, 2, 1, 1, 3, 3, 2 There is interest in determining the center of the cluster identified with the label 2 . By computing this center manually or otherwise, identify which of the following is the correct centroid of this cluster: • Centroid is (5.6, 4.1, 1.2667) • Centroid is (3.5, 6, 1.25) • Centroid is (2.6, 2.9, 4.1) • Centroid is (4.1429, 4.3, 2.0714) • Centroid is (4.7, 4.2, 1.7)
- Explain how to construct representative samples
- The process followed by a variable X is dX = mX dt+sX dz where dz is a Wiener process. What is the coefficient of dt in the process for the square of X i.e. d(X^2)?