Week 4 Summary (DSME5110F)
Mean-variance criterion: prefer
• larger mean (return) • smaller variance (risk)
• Why z-scores?
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– remove the effect of units
– can compare different variables in one dataset
– easier to use the empirical rule and the Chebyshev’s rule
• Two rules:
– empirical rule: normally distributed (bell-shaped) – Chebyshev’s rule: apply to all.
Measure of Association
• covariance: cov()
– can only measure the direction, but not the strength
• correlation coefficient: cor()
– independent of the measurement units used
– linear relationship; does not imply causal relationship – corrplot.mixed()
Counting Rules
• Multiplication principle: n1 × n2 × · · · × nN • Combination Rule: choose(N,n)
Probabilities
• Three methods:
– Classical method
– Relative frequency method – Subjective method
Probability rules
• Complement: P(Ac)=1−P(A)
• P(A∪B)=P(A)+P(B)−P(A∩B)
Conditional Probability
• P(A|B)=P(A∩B);orP(A∩B)=P(A|B)×P(B) P(B)
• Independent: P(A ∩ B) = P(A) × P(B)
Association rules
• What goes with what
• {antecedent} → {consequent}
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