Mbzuai Entry Exam: Sample Questions Link

Given vectors ( u = (1, 2, -1) ), ( v = (0, 1, 3) ). Compute the projection of ( u ) onto ( v ).

Let ( X \sim \mathcalN(0,1) ). Compute ( \mathbbE[e^X] ). (Hint: MGF of normal) mbzuai entry exam sample questions

The exam generally tests: > Python Programming > Basic ML Theory . MBZUAI Entry Exam Sample Questions Section 1: Linear Algebra (30%) Question 1: Let ( A ) be a 3x3 matrix with eigenvalues ( 2, -1, 3 ). What is the determinant of ( A^2 - 2A )? Given vectors ( u = (1, 2, -1) ), ( v = (0, 1, 3) )

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 . Compute ( \mathbbE[e^X] )

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

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?