1.1 Construct sample space of a probabilistic experiment and interpret the axioms of probability.

1.2. Compute probabilities and conditional probabilities from an underlying experiment.

1.3 Solve problems related to Total Probability and Bayes' Theorems.

1.4. Discriminate independent events and compute their probabilities

1.5. Compute probabilities of repeated experiments by using binomial law.

2.1 Determine probability mass function (PMF) and conditional prmf of a discrete random variable (r.v.) from the underlying experiment.

2.2 Compute expected value, and variance of a discrete r.v. from its PMF.

2.3 Calculate the PMF of a discrete r.v. defined as a function of another r.v.

2.4 Obtain the joint PMF of two discrete r.v.'s. and compute marginal PMF’s from the joint PMF.

2.5. Determine independence between discrete r.v's.

3.1 Identify continuous r.v.’s through their probability density (PDF) and cumulative distribution (CDF) functions.

3.2 Compute PDF and CDF for well-known continuous distributions.

3.3 Solve problems using the conditional and joint PDF and CDF.

3.3 Calculate expectation and variance for continuous r.v.’s 

4.1 Solve problems of practical interest through functions of r.v.’s.

4.2 Relate two r.v.’s based on their correlation.

4.3 Utilize transforms of r.v.s in solving particular classes of probability problems. 

4.4 Use limit theorems to estimate probabilities and calculate bounds on some probabilities.