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PROBABILITY

PROBABILITY. CONDITIONAL PROBABILITY. Random variable. A variable defined on a sample space. Fx: The value of a card. Interpretation: A variable that takes different values with different probabilities. (Some) Characteristics of a random variable X: Mean value E(X).

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PROBABILITY

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  1. PROBABILITY

  2. CONDITIONAL PROBABILITY

  3. Random variable • A variable defined on a sample space. Fx: The value of a card. • Interpretation: A variable that takes different values with different probabilities. • (Some) Characteristics of a random variable X: • Mean value E(X). • Variation V(X) = E((X-E(x))^2). Cumulative mass function/distribution function of a random variable: F(x) = P(X ≤ x) Graphical representation by histogram.

  4. BINOMIAL DISTRIBUTION

  5. BINOMIAL DISTRIBUTION

  6. BINOMIAL DISTRIBUTION

  7. POISSON DISTRIBUTION

  8. POISSON DISTRIBUTION

  9. POISSON DISTRIBUTION

  10. CONTINOUS DISTRIBUTIONS

  11. CONTINOUS DISTRIBUTIONS

  12. NORMAL DISTRIBUTION

  13. NORMAL DISTRIBUTION

  14. NORMAL DISTRIBUTION

  15. NORMAL DISTRIBUTION

  16. LOG-NORMAL DISTRIBUTION

  17. Fractile/QQ-plots How can we access information about the distribution of a sample? By comparing fractiles – the QQ-plot in SPSS. The proposed distribution is good, if the fractiles follow a linear pattern. • Notice: • The variability of the points decreases when the sample size increases. • The variation of the points around the line is largest in the ends. Hence, pay more attention to the points in the middle of the plot. • Detrended QQ-plots • The points should be spread evenly above/below the horizontal line. • There should be no pattern.

  18. Examples of QQ-plots QQ-plot QQ-plot QQ-plot Normal distribution Skew distribution Uniform distribution Detrended QQ-plot Detrended QQ-plot Detrended QQ-plot

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