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3 Characteristics of a Random Experiement
- 1. All possible distinct outcomes are known a-priori.
- 2. In any particular trial the outcome is not known a-priori but there is a discernible frequency by which outcomes happen.
- 3. Experiment can be repeated under identical circumstances.
Qualtifications for a random sample
- 1. Independence: the random variables are said to be independent if they do not influence the outcome and are not influenced by the outcome of any other random variable.
- 2. Identically distributed: The RVs (X1,...,Xn) are identically dist. if their density functions are identical in the sense that f(X1 | 0 (theta)) = f(Xn | 0(theta)).
How do you tell if a set is countable?
A set is countable if each element can be matched with a distinct natural number. (1, 2, 3, ...)
What is a subset? A C S? A C S?
- If A & S are sets, we say that A is a subset of S, if every element of A is also an element of S.
- A C S is a strict subset if A =/ S.
- A C S is a weak subset of S if it is possible that A = S
Define Union U
The union of sets A and B denoted A U B, is defined as the set of outcomes that are in A and B (or both).