Lecture 1 Experiments, Models and Probabilities
Dec 19, 2015
Outline
• Definitions• Conditional Probability• Independent Trials– n choose k – multinomial coefficient
• Reliability• Matlab Experiment
Definition
• An outcome of an experiment is any possible observation of that experiment.
• The sample space of an experiment is a set of all possible outcomes.
• An event is a set of outcomes of an experiment.
• An event space is a set of events.
Permutations
• Shuffle the deck and choose three cards in order. How many outcomes are there?– 52 x 51 x 50
Derivation
Assumptions: Four objects A, B, C, and D. Experiment: Choose two objects. How many possible outcomes? =12. Alternative Reasoning: If the order in which objects are drawn is not important (i.e. {A,B}={B,A}), then there are =6 combinations (i.e. {AB,AC,AD,BC,BD,CD}). Each combination has two permutations (i.e. {AB} is distinct from {BA}, if order matters) So 2!=Let n→4, k →2, we have Therefore,
Definitions
• For n trials of a subexperiment with sample space S={s0, ,,,sm-1}, we want to find the number observations sequences in which s0 appears n0 times, s1 appears n1 times, and so on.