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Machine Learning Foundations 06 May 26 - 10 May 2026
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Let 
. That is, 
is distributed uniformly over 
. Define 
. Which of the following is true regarding the random variable 
?
. That is, is distributed uniformly over . Define . Which of the following is true regarding the random variable ?
Consider two functions 
and 
given by: 
Which of the following is true?
and given by: Which of the following is true?- Both
and 
are convex - Only is convex
- Only is convex
- Neither nor is convex
Find all square matrices 
from the given options for which 
is given as: 
where 
.
from the given options for which is given as: where .
Which of the following is/are Hermitian matrices?
, where is a complex square matrix.
, where is a complex square matrix.
, where is a complex matrix, not necessarily square.
, where is a complex square matrix.
Which of the following is/are true?
- A set
is convex if and only if convex-hull 
. - If is a non-empty convex set in
with a finite number of elements, then has exactly one element. - If
is a convex function, then is differentiable. - If
is a function, then the epigraph of is a subset of 
.
Consider a constrained optimization problem in 
with a single inequality constraint as given below: 
Which of the following is/are feasible directions at the point
?
with a single inequality constraint as given below: Which of the following is/are feasible directions at the point
?
The number of automobiles sold weekly at a certain dealership is a random variable with expected value 
. Using Markov's inequality, find the tightest upper bound to the probability that the next week's sales is at least 
. Enter your answer correct to one decimal place. Note that an upper bound of 
is valid but not tight.
. Using Markov's inequality, find the tightest upper bound to the probability that the next week's sales is at least . Enter your answer correct to one decimal place. Note that an upper bound of is valid but not tight.Consider a classifier 
for a binary classification problem as given below:
The dataset has four data-points. 
are the features and 
is the true label:
Find the loss of 
on this dataset and enter your answer correct to two decimal places. Recall that the loss is the average number of misclassified points.
for a binary classification problem as given below:
The dataset has four data-points. are the features and is the true label:
Find the loss of on this dataset and enter your answer correct to two decimal places. Recall that the loss is the average number of misclassified points.Consider a 
matrix with eigenvalues 
and 
. Find the sum of the eigenvalues of the matrix 
. Your answer should be an integer. Note: I is the identity matrix.
matrix with eigenvalues and . Find the sum of the eigenvalues of the matrix . Your answer should be an integer. Note: I is the identity matrix.Let be an exponentially distributed random variable with mean 
. Find the value of 
for which 
. Enter your answer correct to two decimal places.
be an exponentially distributed random variable with mean . Find the value of for which . Enter your answer correct to two decimal places.The joint density function of and is given by:
Compute 
. Enter your answer correct to two decimal places.
and is given by:
Compute . Enter your answer correct to two decimal places.The dataset 
is sampled from a distribution whose PDF is given below with parameter 
:
Assume that each point in the dataset is sampled independently from this distribution. Find the maximum likelihood estimate for . Your answer should be an integer.
is sampled from a distribution whose PDF is given below with parameter :
Assume that each point in the dataset is sampled independently from this distribution. Find the maximum likelihood estimate for . Your answer should be an integer.Aman is evaluating candidates for a Machine Learning role. The time (in hours) taken to complete a technical interview round follows the probability density function:
Find the expected time taken to complete an interview. Your answer should be an integer.
(in hours) taken to complete a technical interview round follows the probability density function:
Find the expected time taken to complete an interview. Your answer should be an integer.Using the method of Lagrange multipliers solve the following constrained optimization problem:
Find the minimum value of the objective function. You can assume that the problem does have a global minimum. Your answer should be an integer.
Find the minimum value of the objective function. You can assume that the problem does have a global minimum. Your answer should be an integer.Answer key
- Q1 (MCQ, 2 marks): A
- Q2 (MCQ, 3 marks): A
- Q3 (MSQ, 3 marks): A, B
- Q4 (MSQ, 3 marks): A, C
- Q5 (MSQ, 3 marks): A, B
- Q6 (MSQ, 3 marks): A, B
- Q7 (SA, 2 marks): 0.79 to 0.81
- Q8 (SA, 2 marks): 0.24 to 0.26
- Q9 (SA, 3 marks): 2
- Q10 (SA, 3 marks): 0.68 to 0.70
- Q11 (SA, 3 marks): 0.32 to 0.34
- Q12 (SA, 3 marks): 8
- Q13 (SA, 3 marks): 2
- Q14 (SA, 4 marks): -2