Probabilistic Analysis Toolkit Purpose Provides expert guidance on analyzing randomized algorithms using probability theory and concentration inequalities. Capabilities - Expected value calculations - Chernoff and Hoeffding bound applications - Markov and Chebyshev inequality analysis - Moment generating function analysis - Concentration inequality selection - Las Vegas and Monte Carlo analysis Usage Guidelines 1. Random Variable Identification : Define relevant random variables 2. Expectation Computation : Calculate expected values 3. Concentration Selection : Choose appropriate bounds 4. Bo…