Mathematical Data Science — DU B.Sc. (Hons.) Mathematics Previous Year Question Papers

Predict - 1 or +1 using a kNN (k-nearest neighbor) classifier with k=3 on x= 3 and x=-1. Name of the 'Course : B.Sc. (H) Mathematics Q1-Q4. and two parts from Q5.-Q6. 3. Parts of the questions to be attempted together. 1. (a) Differentiate between structured and unstructured data. (5) (b) What is preprocessing of data. Explain with the help of an example. (5) (c) Consider the data of coffee shops with following attributes: Name of the coffee shop, Revenue in Rs., Pin code of the shop, Average monthly customers. Briefly explain the attributes as quantitative and qualitative. (5) (d) Define discrete quantitative and continuous quantitative data. Give an example of each. 2. (a) Write five steps of data science and explain these briefly. (5) 6. (a) Consider a matrix A'e R$x4 with squared singular values 0? = 10, 03 = 5; 03 = 2 and o3 = 1. (i) Find the rank of matrix A. (ii) Find the value of lIA - Ali, where Az is the best rank-2 approximation of (b) Draw Voronoi diagram with three points (c) Consider a set of 1 - dimensional data points (b) Use Lloyd's. Algorithm for k-means clustering to divide the following data into two clusters with initial cluster centers C, = (2,1) and C, = (2,3) (c) Reduce the feature 2-dimensional data of the following into one dimensional using Principal Component Analysis (PCA) (b) Explain any two tabular data for mats out of CSV, Excel, Data Frame, XMI or similar. (5) (c) What are anomalies in data science? Explain anomalies with examples. • (5) (d) Give an overview of data source format SQL or 3. (a) State Chebyshev Inequality. Consider a probability density function fand a randoin variable X~f. If E[X] = 20 and Var[X] = 9, find the value of (b) Explain the term probably approximately correct with an example. Consider sets A = {1,2,4,8}. and B = {1,2,3}. Calculate the Jaccard distance between A and B. (5) (c) Define I, distances mathematically and sketch these geometrically for p = 1,2 and oo. (5) (d) Consider two vectors a = (1,2, -4,3, -6) and b = (1,2,5, -2,1) in RS. Find Kullback-Liebler divergence. (5) 4. (a) Find the regression line for the given data height (in): 66 68'60 70 65 61 74 73 75 67 weight (Ibs): 160 170 110 178 155 120 223 215 235 164 (b) Explain polynomial regression, Consider the input -data set with n = 3 points { (2,1), (3,6), (4,5)}. Find polynomial expansion of x generates with p = 5. (5) (c) Define the Gradient in data sciences and find the value of the Gradient for f(x,y,z) = 3x2- 2y3 - 2xe at (3,-2,1). (5) (d) Consider two-variable function f = (x- 5)? + (y + 2)2 - 2xy. Starting with (x, y) = (0,2), using the gradient descent algorithm for the function, perform 3 iterations and report the function value at the end of each step. (5) 5. (a) Find Singular Value Decomposition (SVD) of the