Curriculum Information

Essentials of Calculus:

Sets and operations on sets, series, differential and integral calculus.

Probability:

Sample space and events, probability axioms, counting, independence, total probability theorem and Bayes’ theorem.

Discrete Random Variables:

Probability mass functions (PMFs), functions of random variables, expectation and variance; Bernoulli, binomial, Poisson and geometric random variables. Joint PMFs, conditioning and independence.

Continuous Random Variables:

Probability density functions (PDFs), cumulative density functions, expectation and variance; Uniform, Exponential and Normal random variables. Joint PDFs, conditioning and independence.

Further topics on random variables:

Derived distributions, covariance and correlation, conditional expectation and variance.

Limit theorems:

Markov and Chebyshev inequalities, law of large numbers, central limit theorem.

Statistical inference:

Parametric statistical models, parametric estimation and confidence intervals, hypotheses testing, null and alternative hypotheses, levels and p-values; inferences for a population mean using Normal and t-distributions. Inferences for a population variance using the F-distribution. Goodness of fit tests. Inferences for differences between population means and variances using Normal, t- and F-distributions.