probability. conditional probability random variable a variable defined on a sample space. fx: the...
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![Page 1: PROBABILITY. CONDITIONAL PROBABILITY Random variable A variable defined on a sample space. Fx: The value of a card. Interpretation: A variable that takes](https://reader036.vdocuments.us/reader036/viewer/2022062320/56649d2a5503460f949ff864/html5/thumbnails/1.jpg)
PROBABILITY
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CONDITIONAL PROBABILITY
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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).
Graphical representation by histogram.
Cumulative mass function/distribution function of a random variable:F(x) = P(X ≤ x)
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BINOMIAL DISTRIBUTION
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BINOMIAL DISTRIBUTION
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BINOMIAL DISTRIBUTION
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POISSON DISTRIBUTION
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POISSON DISTRIBUTION
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POISSON DISTRIBUTION
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CONTINOUS DISTRIBUTIONS
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CONTINOUS DISTRIBUTIONS
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NORMAL DISTRIBUTION
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NORMAL DISTRIBUTION
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NORMAL DISTRIBUTION
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NORMAL DISTRIBUTION
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LOG-NORMAL DISTRIBUTION
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Fractile/QQ-plotsHow 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.
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Examples of QQ-plots
Normal distribution Skew distribution Uniform distribution
QQ-plot QQ-plotQQ-plot
Detrended QQ-plot Detrended QQ-plotDetrended QQ-plot