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Chapter 1-General Probability Reading 1 Question 4

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.