Home / Past papers / MLF End Term / this paper
Machine Learning - Bs In Data Science/ Electronic Systems Foundations 13 Sep 26 - 13 Sep 2026
Elapsed 00:00
Consider the following least-squares problem:
where
Suppose one least-squares solution is
Which of the following is/are correct?
where
Suppose one least-squares solution is
Which of the following is/are correct?- The least-squares solution is unique.
- There are infinitely many least-squares solutions.
- The vectors produce exactly the same predictions.
is invertible.
Consider a 
matrix 
satisfying
If trace and determinant of are 9 and 20 respectively, which of the following statements is/are necessarily true?
matrix satisfying
If trace and determinant of are 9 and 20 respectively, which of the following statements is/are necessarily true?- The matrix
is singular. - The trace of
is 
. - The matrix
is singular. - The determinant of
is 
.
Find the minimum distance between the point 
and the plane 
Enter your answer correct to two decimal places.
and the plane Enter your answer correct to two decimal places.Let 
Find the value of 
such that
Find the value of such that
A delivery company records the time 
(in hours) required to deliver a package. The delivery time has the PDF
Under a new routing system, the delivery time becomes 
What is the expected delivery time under the new routing system?
(in hours) required to deliver a package. The delivery time has the PDF
Under a new routing system, the delivery time becomes What is the expected delivery time under the new routing system?Consider the function 
Which of the following is true?
Which of the following is true?
is convex on 
.- is concave on .
- is convex for
and concave for 
. - is neither convex nor concave on any interval.
Let be a discrete random variable such that 
with 
where 
is an unknown parameter. Consider the random sample 
from . The maximum likelihood estimate of 
is:
be a discrete random variable such that with where is an unknown parameter. Consider the random sample from . The maximum likelihood estimate of is:
Let 
where 
and 
are independent. Define 
Which of the following is the value of 
where and are independent. Define Which of the following is the value of 
Consider a constrained optimization problem in 
with a single inequality constraint: 
At the point 
which of the following is/are feasible directions at 
with a single inequality constraint: At the point which of the following is/are feasible directions at 
Consider the function
where 
is a constant. Which of the following is/are true?
where is a constant. Which of the following is/are true?- is continuous at
for 
. - is continuous at for
. - is differentiable at for .
- is not differentiable at for .
Let 
be a Hermitian matrix whose eigenvalues are 
Which of the following statements is/are necessarily true?
be a Hermitian matrix whose eigenvalues are Which of the following statements is/are necessarily true?- is positive definite.
- There exists a nonzero vector
such that 
, where 
denotes the conjugate transpose of 
. - is invertible.
is Hermitian.
A nonnegative random variable satisfies 
Using Markov's inequality, find the smallest value of 
such that 
Enter your answer as an integer.
satisfies Using Markov's inequality, find the smallest value of such that Enter your answer as an integer.Comprehension passage - the questions below it refer to this
Suppose is a real 
matrix with singular values 
Based on the above data, answer the given subquestions.What is the sum of the eigenvalues of 
Inscript What is the rank of 
Answer key
- Q1 (MSQ, 4 marks): B, C
- Q2 (MSQ, 4 marks): A, B, D
- Q3 (SA, 3 marks): 1.70 to 1.76
- Q4 (SA, 3 marks): 8
- Q5 (SA, 3 marks): 7
- Q6 (MCQ, 3 marks): C
- Q7 (MCQ, 3 marks): A
- Q8 (MCQ, 3 marks): C
- Q9 (MSQ, 3 marks): A, B, D
- Q10 (MSQ, 3 marks): B, D
- Q11 (MSQ, 3 marks): B, C, D
- Q12 (SA, 2 marks): 80
- Q13 (SA, 2 marks): 34
- Q14 (SA, 1 marks): 2