Are you looking for NPTEL Introduction to Machine Learning Assignment Week 0 Answers? If yes, you will find the answers to the questions asked in the NPTEL Introduction to Machine Learning quiz exam here. If you are preparing for this exam this article will help you in finding the latest and updated answers.

There is a total of 15 questions related to Probability Theory, Linear Algebra, and Convex Optimization. The correct answers are marked in Green Color with a tick sign.

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NPTEL Introduction to Machine Learning Assignment Week 0 Answers

1. 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:

  • the second ball is red;
  • the second ball is red, given that the first is red.
  1. 1/3, 2/3
  2. 1/2, 1/3
  3. 1/2, 2/3
  4. 1/3, 1/3

2. 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?

  1. 0.803
  2. 0.976
  3. 0.02
  4. 0.204

3. 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?

(Hint: First find the mass function of the number of heads observed in the second round.)

  1. 0.372
  2. 0.055
  3. 0.0345
  4. 0.0488

4. 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?

  1. 0.5101
  2. 0.81
  3. 0.6308
  4. 0.7405

5. 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) < ∞ ?

  1. α < 1/2
  2. α < 1
  3. α > 1
  4. α > 3/4

6. 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.

  1. No, not a monotonic function
  2. Yes, x−2e−1/x, x > 0
  3. No, not right continuous
  4. Yes, x−1e−1/x, x > 0

7. Let Am×n be a matrix of real numbers. The matrix AAT has an eigenvector x with eigenvalue b. Then the eigenvector y of AT A which has eigenvalue b is equal to

  1. AT Ax
  2. AT x
  3. x
  4. Cannot be described in terms of x

8. Let An×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?

  1. |b| > 1
  2. |b| <= 1
  3. |b| >= 1
  4. |b| < 1

9. Let u be a n × 1 vector, such that uT u = 1. Let I be the n × n identity matrix. The n × n matrix A is given by (I − kuuT), where k is a real constant. u itself is an eigenvector of A, with eigenvalue -1. What is the value of k?

  1. -2
  2. -1
  3. 2
  4. 0

10. Which of the following are true for any m × n matrix A of real numbers?

  1. The rowspace of A is the same as the columnspace of AT
  2. The rowspace of A is the same as the rowspace of AT
  3. The eigenvectors of AAT are the same as the eigenvectors of AT A
  4. The eigenvalues of AAT are the same as the eigenvalues of AT A

11. The Singular Value Decomposition (SVD) of a matrix R is given by USVT. Consider an orthogonal matrix Q and A = QR. The SVD of A is given by U1S1V 1T. Which of the following is/are true?

  1. U = U1
  2. S = S1
  3. V = V

12. Consider two random variables X and Y having joint density function f(x,y)=2e−x−y,0<x<y<∞. Are X and Y independent? Find the covariance of X and Y.

  1. Yes, 1/4
  2. Yes 1/2
  3. No, 1/4
  4. No, 1/2

13. Is the following a distribution function? f(x) = {0e-1/x x>0 otherwise, If so, give the corresponding density function. If not, mention why it is not, mention why it is not a distribution function.

  1. No, not a monotonic function
  2. Yes, x-2e-1/x , x>0
  3. No, not right continuous
  4. Yes, x-1e-1/x, x>0

14. Can the value of a probability density function be greater than one? What about the cumulative distribution function?

  1. PDF: yes, CDF: yes
  2. PDF: yes, CDF: no
  3. PDF: no, CDF: yes
  4. PDF: no, CDF: no

15. You are given a biased coin with probability of seeing a head is p=0.6 and probability of seeing a tail is q=0.4. Suppose you toss the coin 10 times, what is the probability of you getting the head at most 2 times? Also, what is the probability of you getting the head for the first time on your fourth attempt?

  1. 0.012, 0.038
  2. 0.054, 0.038
  3. 0.012, 0.064
  4. 0.054, 0.064
NPTEL Introduction to Machine Learning Assignment Answers

FAQ

What is NPTEL Introduction to Machine Learning?

NPTEL Introduction to Machine Learning Course is an online free course by IIT Madras that has been developed by Prof. Balaraman Ravindran. The main aim of this course is to provide the basic concepts of machine learning from a mathematically well-motivated perspective.

Are These Answers Correct?

Yes, all these answers are 100% correct.

Are These Answers Updated?

Yes, these answers are up to date with the latest questions.

Will I Get a Certificate?

Yes, you will get a certificate but it costs ₹1000 exam fee.

Wrap Up

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