Mbzuai Entry Exam Sample Questions May 2026

Given a binary classifier with confusion matrix: TP=90, FN=10, FP=30, TN=70 Compute Precision , Recall , F1-score , and Accuracy .

def func(x, lst=[]): lst.append(x) return lst print(func(1)) print(func(2)) Write a Python function normalize(X) that takes a 2D numpy array X (samples × features) and returns a zero-mean, unit-variance normalized version (feature-wise). Do not use sklearn . mbzuai entry exam sample questions

Let ( X \sim \mathcalN(0,1) ). Compute ( \mathbbE[e^X] ). (Hint: MGF of normal) Given a binary classifier with confusion matrix: TP=90,

Briefly explain how backpropagation computes gradients in a neural network. Why is the chain rule essential? Section 5: Python & Coding Logic (10%) Question 13: What is the output of the following? Let ( X \sim \mathcalN(0,1) )

If ( A ) and ( B ) are square invertible matrices, then ( (A + B)^-1 = A^-1 + B^-1 ). Explain briefly. Section 2: Calculus & Optimization (25%) Question 4: Find the gradient ( \nabla f(x,y) ) of ( f(x,y) = \ln(1 + e^xy) ). Then compute the directional derivative at ( (1,0) ) in the direction of ( (1,1) ).