Introduction to Probability
1a. Models, experiments, sets
1. Sets and probabilities
Probabilistic models of random experiments. Compound experiments. Sampling experiments.
[Si] "Prob. Spaces" : Sect 1
"Random experiments"
.
[BT] Sect 1.2 "Probabilistic models" (excluding Item "Continuous models").
Events as subsets of the sample space.
[Si] "Prob. Spaces" : Sect 2 "Events and random variables" : Item
"Sample spaces and events"
.
[BT] Sect 1.2 "Probabilistic models" (excluding Item "Continuous models").
Random variables as functions. Basic and derived variables. Indicators.
[Si] "Prob. Spaces" : Sect 2 "Events and random variables" : Item "Random variables", especially
"Basic and derived variables"
.
[BT] Sect 2.1 "Basic concepts".
Algebra of sets: operations, relations, rules.
[Si] "Foundations" : Sect 1 "Sets" : Items
"Sets and subsets"
,
"Set operations"
,
"Basic rules"
.
[BT] Sect 1.1 "Sets".
Compound experiments and product sets.
[Si] "Prob. Spaces" : Sect 2 "Events and random variables" : Item
"Sample spaces and events"
.
[Si] "Foundations" : Sect 1 "Sets" : Item
"Product sets"
(also "Rules for product sets").
Unordered samples and sets of subsets.
[Si] "Finite sampling models" : Sect 1 "Introduction" : Item
"The unordered sample"
.
Ordered samples and sets of sequences.
[Si] "Finite sampling models" : Sect 1 "Introduction" : Items
"Sampling models"
,
"The exchangeable property"
.
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