Mbzuai Entry Exam Sample Questions Fix [COMPLETE ★]

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

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

For ( f(x) = \frac12 |Ax - b|^2 ), derive the closed-form solution for ( x ) that minimizes ( f ). Section 3: Probability & Statistics (20%) Question 7: You have two dice: one fair, one loaded (shows 6 with probability ( 1/3 ), others each ( 2/15 )). You pick a die at random (50% chance each), roll it once, and get a 6. What is the probability it was the loaded die? Given vectors ( u = (1, 2, -1) ), ( v = (0, 1, 3) )

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? For ( f(x) = \frac12 |Ax - b|^2