If you are serious about passing, do not just read the answers. Use this schedule:
Many applicants waste time on irrelevant topics. MBZUAI does not include:
If you see a question about a specific neural network layer, it is a math question in disguise (e.g., "A linear layer with weight matrix W... compute the gradient").
Question 3 (Bayes for NLP) In a spam detection model, 20% of emails are spam. The word "winner" appears in 60% of spam emails but only 5% of non-spam emails.
Question 4 (Convergence & Distributions) Let ( Z_1, Z_2, ..., Z_n ) be i.i.d. random variables with mean ( \mu ) and variance ( \sigma^2 ). Define the sample mean ( \barZ_n ).
MBZUAI insight: The exam frequently connects pure statistics to optimization. They want you to know that CLT explains why the noisy gradient (from a mini-batch) approximates the true gradient.
The MBZUAI entrance exam assesses foundational knowledge in: mbzuai entry exam sample questions best
It is required for MSc and PhD applicants (waivers possible for exceptional backgrounds). The exam is computer‑based, multiple‑choice, and typically 2–3 hours.
Probability & statistics
Discrete math & logic
Algorithms & programming (pseudo-code acceptable)
Machine learning fundamentals
Short answer / reasoning
Best question type: Bayes’ theorem and expectation.
Sample Q1 (Bayes):
A medical test has 99% sensitivity and 95% specificity. Disease prevalence = 1%. If a person tests positive, what is the probability they actually have the disease? Show all steps.
Sample Q2 (MLE):
Suppose ( x_1, x_2, ..., x_n ) are i.i.d. from ( P(x|\lambda) = \lambda e^-\lambda x ) (exponential). Derive the Maximum Likelihood Estimator for ( \lambda ).
Attention mechanisms and PCA rely on linear algebra. MBZUAI expects speed with matrix operations. If you are serious about passing, do not
Sample Question 3: Eigenvalues of a Special Matrix
Let ( J ) be an ( n \times n ) matrix of all ones. Let ( I ) be the identity. Consider ( A = 2I + 3J ). What is the sum of all eigenvalues of ( A )?
Solution Reasoning: The sum of eigenvalues = Trace(A). Trace(A) = sum of diagonal entries.
Sample Question 4: Orthogonal Projections
Given a vector ( v = [3, 4]^T ) in ( \mathbbR^2 ), what is the matrix ( P ) that projects any vector onto the line spanned by ( v )?
Solution Reasoning: Projection matrix onto a vector ( v ) is ( P = \fracv v^Tv^T v ). ( v v^T = \beginbmatrix 9 & 12 \ 12 & 16 \endbmatrix ). ( v^T v = 25 ). Thus ( P = \frac125\beginbmatrix 9 & 12 \ 12 & 16 \endbmatrix ). Correct answer: A Many applicants waste time on irrelevant topics