Problem 1 (25 Points): Differential Privacy and Composition Theorems Task 1: Sensitivity (11 Points): Given a dataset of salaries, and assume that all numbers are in the range (0,900K]. What is the sensitivity of each of the following query? - 1 Point. The number of people with salary above 100K. - 2 Points. The histogram of the number of people with salary in each of (0,100K],(100K,200K],,(800K,900K - 2 Points. The histogram of the number of people with salary in each of (0,10K],(10K,20K],,(890K,900K]. - 2 Points. Sum of total salary. - 2 Points. The medium salary. - 2 Points. The mode, i.e., the number which appears most often in the set. Task 2: Error and variance for Randomized Response (8 Points). Derive the expected error and variance of the best estimate hat shown in the Slide 38 (each 4 points). Task 3: Composition Theorems Proofs (6 Points). In the class, we have shown the proof of -Differential Privacy for the Sequential Composition theorem. Following that, prove for the Parallel Composition and Postprocessing theorems (each 3 points)