Quiz Space

Machine Learning Foundations · End Term · 21 Dec 2025 · September 2025 term

Question 32: A company aims to minimize its production cost, represen…

Question 32

+3 marksWritten answer

A company aims to minimize its production cost, represented by the following quadratic function: The company applies the gradient descent algorithm to minimize this function, starting with an initial guess of and using a step size (learning rate) of

, where Based on the above data, answer the given subquestions.

A company aims to minimize its production cost, represented by the following quadratic function: The company applies th

Compute the value of after the second iteration, i.e., .

Show answer

A written answer, not marked automatically.

See the whole paperTake it as a mock test

Question 32 of 38 in the IIT Madras BS Machine Learning Foundations (MLF) End Term paper sat on 21 Dec 2025, in the September 2025 term (Machine Learning Foundations 18 Dec 25). It carries 3 marks.

More questions from this paper

  1. Q1Consider the function defined as . For what values of is convex
  2. Q2A real estate company wants to create a model to predict house prices based on the size of the house. They collect data…
  3. Q3Which of the following is/are true
  4. Q4Let . Find the directional derivative of at the point in the direction of unit vector along .
  5. Q5An ML team wants to predict whether an email is spam or not by using some classification models. Therefore, the team de…
  6. Q6Consider the convex hull of the set of points . Which of the following points belongs to the convex hull?
  7. Q7Let be a continuous random variable with the probability density function: What is the value of
  8. Q8If is a square invertible matrix, which of the following is/are true?
  9. Q9is a matrix whose eigenvalues are . Consider the set as defined below: Find .
  10. Q10An analyst monitors the number of defective items produced daily. Let denote number of defective items produced in a da…
  11. Q11Using the method of Lagrange multipliers, find a point on the circle centered at with radius that is closest to the poi…
  12. Q12Consider two datasets in , and , each having three points as shown below. The figure is drawn to scale. PCA is run on b…
  13. Q13Find the waiting time such that 95% of customers are served within minutes.
  14. Q14The time (in minutes) a bank employee spends assisting a customer follows an exponential distribution with parameter . …
  15. Q15What is the probability that a randomly chosen customer waits between and minutes
  16. Q16Anil throws a dart onto a circular board. Let a random variable denote the distance from the center to the point where …
  17. Q17Using Chebyshev's inequality, find an upper bound for , where represents the mean of the random variable . Enter your a…
  18. Q18Using the method of Lagrange multipliers, find a point on the circle centered at with radius that is closest to the poi…
  19. Q19Consider the following constrained optimization problem: Answer the sub-questions assuming that we take a very small st…
  20. Q20Consider the following constrained optimization problem: If corresponds to the global minimum, find . Enter your answer…
  21. Q21Consider the following constrained optimization problem: Answer the sub-questions assuming that we take a very small st…
  22. Q22If and , where Based on the above data, answer the given subquestions. What is the distribution of
  23. Q23Consider the following constrained optimization problem: Answer the sub-questions assuming that we take a very small st…
  24. Q24If and , where Based on the above data, answer the given subquestions. What is the distribution of
  25. Q25If and , where Based on the above data, answer the given subquestions. What is the distribution of
  26. Q26If and , where Based on the above data, answer the given subquestions. Find the covariance matrix of .
  27. Q27If and , where Based on the above data, answer the given subquestions. What is the distribution of
  28. Q28A company aims to minimize its production cost, represented by the following quadratic function: The company applies th…
  29. Q29If and , where Based on the above data, answer the given subquestions. Find the covariance matrix of .
  30. Q30A company aims to minimize its production cost, represented by the following quadratic function: The company applies th…
  31. Q31A company aims to minimize its production cost, represented by the following quadratic function: The company applies th…
  32. Q33A cafe records the time (in minutes) a customer waits for a freshly made sandwich. The waiting time follows an exponent…
  33. Q34Consider the following constrained optimization problem: Answer the sub-questions assuming that we take a very small st…
  34. Q35If and , where Based on the above data, answer the given subquestions.
  35. Q36A company aims to minimize its production cost, represented by the following quadratic function: The company applies th…
  36. Q37If and , where Based on the above data, answer the given subquestions.
  37. Q38A company aims to minimize its production cost, represented by the following quadratic function: The company applies th…