Probabilité : Exercices corrigés (Broché) by Hervé Carrieu

By Hervé Carrieu

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15. ) The data consist of average ratings over the course of treatment for patients undergoing radiotherapy. Variables measured include x 1 (number of symptoms, such as sore throat or nausea); x 2 (amount of activity, on a 1–5 scale); x 3 (amount of sleep, on a 1–5 scale); x 4 (amount of food consumed, on a 1–3 scale); x 5 (appetite, on a 1–5 scale); and x 6 (skin reaction, on a 0–3 scale). (a) Construct the two-dimensional scatter plot for variables x 2 and x 3 and the marginal dot diagrams (or histograms).

B) Infer the sign of the sample covariance s1 2 from the scatter plot. (c) Compute the sample means x– 1 and x– 2 and the sample variances s1 1 and s2 2 . Compute the sample covariance s1 2 and the sample correlation coefficient r1 2 . Interpret these quantities. (d) Display the sample mean array x–, the sample variance-covariance array Sn , and the sample correlation array R using (1-8). 3. The following are five measurements on the variables x 1 , x 2 , and x 3 : x1 9 2 6 5 8 x2 12 8 6 4 10 x3 3 4 0 2 1 Find the arrays x–, Sn , and R.

Chernoff [4] suggested representing p-dimensional observations as a two-dimensional face whose characteristics (face shape, mouth curvature, nose length, eye size, pupil position, and so forth) are determined by the measurements on the p variables. 27 28 Chapter 1 Aspects of Multivariate Analysis As originally designed, Chernoff faces can handle up to 18 variables. The assignment of variables to facial features is done by the experimenter, and different choices produce different results. Some iteration is usually necessary before satisfactory representations are achieved.

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