 ## Consider two random variables X and Y having joint density function f(x,y)=2^e−x−y,0 ## The Singular Value Decomposition (SVD) of a matrix R is given by USV^T. Consider an orthogonal matrix Q and A = QR. The SVD of A is given by U₁S₁V₁^T. Which of the following is/are true? ## Which of the following are true for any m × n matrix A of real numbers? ## Let u be a n × 1 vector, such that u^T u = 1. Let I be the n × n identity matrix. The n × n matrix A is given by (I − kuu^T), where k is a real constant. u itself is an eigenvector of A, with eigenvalue -1. What is the value of k? ## Let A^n×n be a row stochastic matrix – in other words, all elements are non-negative and the sum of elements in every row is 1. Let b be an eigenvalue of A. Which of the following is true? ## Let A^m×n be a matrix of real numbers. The matrix AA^T has an eigenvector x with eigenvalue b. Then the eigenvector y of A^T A which has eigenvalue b is equal to ## Is the following a distribution function? F(x) = {0^e-2 e-1/x x>0 otherwise . If so, give the corresponding density function. If not, mention why it is not a distribution function. ## Let X have mass function f(x)={0{x(x+1)}-1 . If x=1, 2, …, otherwise, and let α ∈ R. For what values of α is it the case that E(Xα) < ∞ ? ## An airline knows that 5 percent of the people making reservations on a certain flight will not show up. Consequently, their policy is to sell 52 tickets for a flight that can hold only 50 passengers. What is the probability that there will be a seat available for every passenger who shows up? ## In an experiment, n coins are tossed, with each one showing up heads with probability p independently of the others. Each of the coins which shows up heads is then tossed again. What is the probability of observing 5 heads in the second round of tosses, if we toss 15 coins in the first round and p = 0.4? ## A medical company touts its new test for a certain genetic disorder. The false negative rate is small: if you have the disorder, the probability that the test returns a positive result is 0.999. The false positive rate is also small: if you do not have the disorder, the probability that the test returns a positive result is only 0.005. Assume that 2% of the population has the disorder. If a person chosen uniformly from the population is tested and the result comes back positive, what is the probability that the person has the disorder? ## There are n bins of which the kth contains k − 1 blue balls and n − k red balls. You pick a bin at random and remove two balls at random without replacement. Find the probability that: ## NPTEL Introduction to Machine Learning Assignment Week 0 Answers ## NPTEL Introduction to Machine Learning Assignment Answers [Week 0-12] ## NPTEL Introduction to Machine Learning Assignment Week 12 Answers ## NPTEL Introduction to Machine Learning Assignment Week 11 Answers ## NPTEL Introduction to Machine Learning Assignment Week 1 Answers ## NPTEL Introduction to Machine Learning Assignment Week 8 Answers ## NPTEL Introduction to Machine Learning Assignment Week 7 Answers ## NPTEL Introduction to Machine Learning Assignment Week 6 Answers ## NPTEL Introduction to Machine Learning Assignment Week 5 Answers ## NPTEL Introduction to Machine Learning Assignment Week 4 Answers ## NPTEL Introduction to Machine Learning Assignment Week 3 Answers ## NPTEL Introduction to Machine Learning Assignment Week 2 Answers ## NPTEL Introduction to Machine Learning Assignment Week 10 Answers 