Statistical Methods for Business and economics summary - Tilburg university - Economics
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Statistics for ECO
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Tilburg University (UVT)
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Statistical Methods for Business and Economics
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Summary for the course ''Statistics'. This summary was written in order to study for the midterm as well as for the final. Everything you need to know is available in this summary.
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SPSS Guideline and Hypotheses Testing for Regressions
Samenvatting: Data-Analyse
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Economics
Statistics for ECO
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STATISTICS FOR ECO:
SUMMARY
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1
,Statistics summary
6.1 Random experiments
Random experiment: an experiment for which the outcome is determined by chance
Sample space (Ω): set of all N possible outcomes
Venn diagram:
Events: subsets of the sample space
Single events: events with one specific outcome (BBB or AAA or BCB or CBB etc.)
Multiple events: more than one outcome (BBB, AAA and CBB or BCC, ABB and AAC etc.)
Empty event: does not occur (empty set)
6.2 Rules for sets / events
1. A c B A is subset of B if A occurs, then B occurs
2. A-complement complement of A A does not occur
3. A u B union of A and B A or B occurs (or both)
4. A ∩ B intersection of A and B A and B occur
5. A ∩ B = disjoint A and B are disjoint no common outcomes
6.3 Historical definitions of probability
2
,* Classical definition of probability:
Requirement: all outcomes of the experiment are equally likely
Properties:
- 0 ≤ P(A) ≤ 1
- P(disjoint) = 0 and P(Ω) = 1
- P(A u B) = P(A) + P(B) If A and B are disjoint!
* Empirical definition of probability:
Requirement: the experiment is independently and identically repeatable
Independently: the experiment don’t influence each other
Identically: the probabilities remain the same
Properties:
- 0 ≤ P(A) ≤ 1
- P(disjoint) = 0 and P(Ω) = 1
- P(A u B) = P(A) + P(B) If A and B are disjoint!
* Subjective definition of probability:
Can be used for all random experiments
Disadvantage: it is subjective
Properties:
- 0 ≤ P(A) ≤ 1
- P(disjoint) = 0 and P(Ω) = 1
- P(A u B) = P(A) + P(B) If A and B are disjoint!
3
, 7.1 Basic properties of model P (axioms)
1. P(A-complement) = 1 – P(A)
2. P(disjoint) = 0
3. A c B = P(A) ≤ P(B)
4. P(A) = P(A ∩ B) + P(A ∩ B-complement)
5. /
6. P(A u B) = P(A) + P(B) – P(A ∩ B)
7.2 Rules for counting
1. # orderings of k objects
k! = k factorial e.g. 🡪 4! = 4 * 3 * 2 * 1 = 24
0! = 1 (by definition)
2. # possibilities to choose k objects from m objects
Ordered: in a specific order
With replacement: you can pick the same k for several places
Without replacement: you can only put the same k in 1 place
2a. Ordered, with replacement
2b. Ordered, without replacement
2c. Unordered, without replacement
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