Probability Stochastic Process (V-U)

• Introduction to Probability and Stochastic Processes (V-U)
• Set Theory (V-U)
• Relations, Functions, Probability (V-U)
• Probability Experiments: Repeated, Dependent, Cascaded (V-U)
• Joint Probability, Conditional Probability, Total Probability (V-U)
• Combinatronics, Birthday Problem, Bayes Rule (V-U)
• Bayes Rule Application, Partitioned Footpath, Partioned Floor, Trains on a Junction (V-U)
• Trains on a Junction, A local bus stop, Random line partition (V-U)
• Equally likely outcomes, Random Variables, Chuk-a-luck, Binomial & Poisson Distributions (V-U)
• CDF of Poisson PMF, Joint Distribution Example, Marginal PMF (V-U)
• Conditional Distribution, Conditional PMF, Expected Value, Transformation of Random Variables (V-U)
• Transformation of RVs, Conditional Expectation, Co-variance and Correlation (V-U)
• Continuous Random Variable, Probability Density Function, PDF and CDF of a Continuous RV (V-U)
• CDF of a Continuous RV, CDF and PDF of Nozzle Height, Exponential RV (V-U)
• Failure of TV Set Example, Gaussian RV (V-U)
• Mean of Transformed RV, Height Distribution of Humans Example, Higher Moments (V-U)
• Scaling of Gaussian RV, Standard Gaussian Events, Joint Distributions, Pair of RVs (V-U)
• Pair of RVs , Buffon's Needle, Exponential RV Pair, Pair of Erlang RVs (V-U)
• Exponential RV Pair, Pair of Dependent RVs, Correlation & Covariance (V-U)
• Correlation & Covariance, Correlated Gaussian RVs (V-U)
• Function of two RVs, Evaluation of Fz(Z), CDF & PDF of Z = X + Y (V-U)
• Function of two RVs, Evaluation of Fz(Z), CDF & PDF of Z = Y / X, CDF & PDF of Z = max (X, Y) (V-U)
• Multiple derived RVs, Probability Computation (V-U)
• Direct Computation of Derived CDF (V-U)
• Non-invertible Transformations (V-U)