June 28, 2019 in P
1.a – Define set functions, Venn diagrams, sample space, and events. Define probability as a set function on a collection of events and state the basic axioms of probability.
1.b – Calculate probabilities using addition and multiplication rules.
1.c – Define independence and calculate probabilities of independent events.
1.d – Calculate probabilities of mutually exclusive events.
1.e – Define and calculate conditional probabilities.
1.f – Calculate probabilities using combinatorics, such as combinations and permutations.
1.g – State Bayes Theorem and the law of total probability and use them to calculate conditional probabilities.
2.a-b – Explain and apply the concepts of random variables, probability and probability density functions, cumulative distribution functions. & Calculate conditional probabilities.
2.c – Explain and calculate expected value, mode, median, percentile, and higher moments.
2.d – Explain and calculate variance, standard deviation, and coefficient of variation.
2.e – Define probability generating functions and moment generating functions and use them to calculate probabilities and moments.
2.f – Determine the sum of independent random variables (Poisson and normal).
2.g – Apply transformations.
3.a – Explain and perform calculations concerning joint probability functions, probability density functions, and cumulative distribution functions.
3.b – Determine conditional and marginal probability functions, probability density functions, and cumulative distribution functions.
3.c – Calculate moments for joint, conditional, and marginal random variables.
3.d – Explain and apply joint moment generating functions.
3.e – Calculate variance, standard deviation for conditional and marginal probability distributions.
3.f – Calculate joint moments, such as the covariance and the correlation coefficient.
3.g – Determine the distribution of a transformation of jointly distributed random variables. & Determine the distribution of order statistics from a set of independent random variables.
3.h – Calculate probabilities and moments for linear combinations of independent random variables.
3.i – State and apply the Central Limit Theorem.